diff --git a/plugin/trino-mysql/pom.xml b/plugin/trino-mysql/pom.xml
index 3751817e19a8..1a61d6fdf7b2 100644
--- a/plugin/trino-mysql/pom.xml
+++ b/plugin/trino-mysql/pom.xml
@@ -160,6 +160,12 @@
             <scope>test</scope>
         </dependency>
 
+        <dependency>
+            <groupId>io.trino</groupId>
+            <artifactId>trino-parser</artifactId>
+            <scope>test</scope>
+        </dependency>
+
         <dependency>
             <groupId>io.trino</groupId>
             <artifactId>trino-plugin-toolkit</artifactId>
diff --git a/plugin/trino-mysql/src/main/java/io/trino/plugin/mysql/MySqlClient.java b/plugin/trino-mysql/src/main/java/io/trino/plugin/mysql/MySqlClient.java
index 14d86597eaf2..ca4475b9e245 100644
--- a/plugin/trino-mysql/src/main/java/io/trino/plugin/mysql/MySqlClient.java
+++ b/plugin/trino-mysql/src/main/java/io/trino/plugin/mysql/MySqlClient.java
@@ -270,6 +270,7 @@ public MySqlClient(
 
         this.connectorExpressionRewriter = JdbcConnectorExpressionRewriterBuilder.newBuilder()
                 .addStandardRules(this::quoted)
+                .withTypeClass("integer_type", ImmutableSet.of("tinyint", "smallint", "integer", "bigint"))
                 // No "real" on the list; pushdown on REAL is disabled also in toColumnMapping
                 .withTypeClass("numeric_type", ImmutableSet.of("tinyint", "smallint", "integer", "bigint", "decimal", "double"))
                 .map("$equal(left: numeric_type, right: numeric_type)").to("left = right")
@@ -279,8 +280,17 @@ public MySqlClient(
                 .map("$less_than_or_equal(left: numeric_type, right: numeric_type)").to("left <= right")
                 .map("$greater_than(left: numeric_type, right: numeric_type)").to("left > right")
                 .map("$greater_than_or_equal(left: numeric_type, right: numeric_type)").to("left >= right")
+                .map("$add(left: integer_type, right: integer_type)").to("left + right")
+                .map("$subtract(left: integer_type, right: integer_type)").to("left - right")
+                .map("$multiply(left: integer_type, right: integer_type)").to("left * right")
+                .map("$divide(left: integer_type, right: integer_type)").to("left / right")
+                .map("$modulus(left: integer_type, right: integer_type)").to("left % right")
+                .map("$negate(value: integer_type)").to("-value")
                 .add(new RewriteLikeWithCaseSensitivity())
                 .add(new RewriteLikeEscapeWithCaseSensitivity())
+                .map("$not($is_null(value))").to("value IS NOT NULL")
+                .map("$is_null(value)").to("value IS NULL")
+                .map("$nullif(first, second)").to("NULLIF(first, second)")
                 .build();
 
         JdbcTypeHandle bigintTypeHandle = new JdbcTypeHandle(Types.BIGINT, Optional.of("bigint"), Optional.empty(), Optional.empty(), Optional.empty(), Optional.empty());
diff --git a/plugin/trino-mysql/src/test/java/io/trino/plugin/mysql/TestMySqlClient.java b/plugin/trino-mysql/src/test/java/io/trino/plugin/mysql/TestMySqlClient.java
index 690fcf5f97f7..6462f39267be 100644
--- a/plugin/trino-mysql/src/test/java/io/trino/plugin/mysql/TestMySqlClient.java
+++ b/plugin/trino-mysql/src/test/java/io/trino/plugin/mysql/TestMySqlClient.java
@@ -13,6 +13,7 @@
  */
 package io.trino.plugin.mysql;
 
+import com.google.common.collect.ImmutableMap;
 import io.trino.plugin.base.mapping.DefaultIdentifierMapping;
 import io.trino.plugin.jdbc.BaseJdbcConfig;
 import io.trino.plugin.jdbc.ColumnMapping;
@@ -22,11 +23,25 @@
 import io.trino.plugin.jdbc.JdbcExpression;
 import io.trino.plugin.jdbc.JdbcStatisticsConfig;
 import io.trino.plugin.jdbc.JdbcTypeHandle;
+import io.trino.plugin.jdbc.QueryParameter;
+import io.trino.plugin.jdbc.expression.ParameterizedExpression;
 import io.trino.plugin.jdbc.logging.RemoteQueryModifier;
 import io.trino.spi.connector.AggregateFunction;
 import io.trino.spi.connector.ColumnHandle;
 import io.trino.spi.expression.ConnectorExpression;
 import io.trino.spi.expression.Variable;
+import io.trino.spi.type.Type;
+import io.trino.sql.planner.ConnectorExpressionTranslator;
+import io.trino.sql.planner.LiteralEncoder;
+import io.trino.sql.planner.Symbol;
+import io.trino.sql.planner.TypeProvider;
+import io.trino.sql.tree.ArithmeticBinaryExpression;
+import io.trino.sql.tree.ArithmeticUnaryExpression;
+import io.trino.sql.tree.Expression;
+import io.trino.sql.tree.IsNotNullPredicate;
+import io.trino.sql.tree.IsNullPredicate;
+import io.trino.sql.tree.NullIfExpression;
+import io.trino.sql.tree.SymbolReference;
 import org.junit.jupiter.api.Test;
 
 import java.sql.Types;
@@ -34,11 +49,17 @@
 import java.util.Map;
 import java.util.Optional;
 
+import static com.google.common.collect.ImmutableMap.toImmutableMap;
+import static io.trino.SessionTestUtils.TEST_SESSION;
 import static io.trino.spi.type.BigintType.BIGINT;
 import static io.trino.spi.type.BooleanType.BOOLEAN;
 import static io.trino.spi.type.DoubleType.DOUBLE;
+import static io.trino.spi.type.VarcharType.createVarcharType;
+import static io.trino.sql.planner.TestingPlannerContext.PLANNER_CONTEXT;
+import static io.trino.sql.planner.TypeAnalyzer.createTestingTypeAnalyzer;
 import static io.trino.testing.TestingConnectorSession.SESSION;
 import static io.trino.type.InternalTypeManager.TESTING_TYPE_MANAGER;
+import static java.lang.String.format;
 import static org.assertj.core.api.Assertions.assertThat;
 
 public class TestMySqlClient
@@ -57,6 +78,13 @@ public class TestMySqlClient
                     .setJdbcTypeHandle(new JdbcTypeHandle(Types.DOUBLE, Optional.of("double"), Optional.empty(), Optional.empty(), Optional.empty(), Optional.empty()))
                     .build();
 
+    private static final JdbcColumnHandle VARCHAR_COLUMN =
+            JdbcColumnHandle.builder()
+                    .setColumnName("c_varchar")
+                    .setColumnType(createVarcharType(10))
+                    .setJdbcTypeHandle(new JdbcTypeHandle(Types.VARCHAR, Optional.of("varchar"), Optional.of(10), Optional.empty(), Optional.empty(), Optional.empty()))
+                    .build();
+
     private static final JdbcClient JDBC_CLIENT = new MySqlClient(
             new BaseJdbcConfig(),
             new JdbcStatisticsConfig(),
@@ -68,6 +96,8 @@ public class TestMySqlClient
             new DefaultIdentifierMapping(),
             RemoteQueryModifier.NONE);
 
+    private static final LiteralEncoder LITERAL_ENCODER = new LiteralEncoder(PLANNER_CONTEXT);
+
     @Test
     public void testImplementCount()
     {
@@ -169,4 +199,99 @@ private static void testImplementAggregation(AggregateFunction aggregateFunction
                     .isEqualTo(aggregateFunction.getOutputType());
         }
     }
+
+    @Test
+    public void testConvertArithmeticBinary()
+    {
+        for (ArithmeticBinaryExpression.Operator operator : ArithmeticBinaryExpression.Operator.values()) {
+            ParameterizedExpression converted = JDBC_CLIENT.convertPredicate(
+                            SESSION,
+                            translateToConnectorExpression(
+                                    new ArithmeticBinaryExpression(
+                                            operator,
+                                            new SymbolReference("c_bigint_symbol"),
+                                            LITERAL_ENCODER.toExpression(42L, BIGINT)),
+                                    Map.of("c_bigint_symbol", BIGINT)),
+                            Map.of("c_bigint_symbol", BIGINT_COLUMN))
+                    .orElseThrow();
+
+            assertThat(converted.expression()).isEqualTo(format("(`c_bigint`) %s (?)", operator.getValue()));
+            assertThat(converted.parameters()).isEqualTo(List.of(new QueryParameter(BIGINT, Optional.of(42L))));
+        }
+    }
+
+    @Test
+    public void testConvertArithmeticUnaryMinus()
+    {
+        ParameterizedExpression converted = JDBC_CLIENT.convertPredicate(
+                        SESSION,
+                        translateToConnectorExpression(
+                                new ArithmeticUnaryExpression(
+                                        ArithmeticUnaryExpression.Sign.MINUS,
+                                        new SymbolReference("c_bigint_symbol")),
+                                Map.of("c_bigint_symbol", BIGINT)),
+                        Map.of("c_bigint_symbol", BIGINT_COLUMN))
+                .orElseThrow();
+
+        assertThat(converted.expression()).isEqualTo("-(`c_bigint`)");
+        assertThat(converted.parameters()).isEqualTo(List.of());
+    }
+
+    @Test
+    public void testConvertIsNull()
+    {
+        // c_varchar IS NULL
+        ParameterizedExpression converted = JDBC_CLIENT.convertPredicate(SESSION,
+                        translateToConnectorExpression(
+                                new IsNullPredicate(
+                                        new SymbolReference("c_varchar_symbol")),
+                                Map.of("c_varchar_symbol", VARCHAR_COLUMN.getColumnType())),
+                        Map.of("c_varchar_symbol", VARCHAR_COLUMN))
+                .orElseThrow();
+        assertThat(converted.expression()).isEqualTo("(`c_varchar`) IS NULL");
+        assertThat(converted.parameters()).isEqualTo(List.of());
+    }
+
+    @Test
+    public void testConvertIsNotNull()
+    {
+        // c_varchar IS NOT NULL
+        ParameterizedExpression converted = JDBC_CLIENT.convertPredicate(SESSION,
+                        translateToConnectorExpression(
+                                new IsNotNullPredicate(
+                                        new SymbolReference("c_varchar_symbol")),
+                                Map.of("c_varchar_symbol", VARCHAR_COLUMN.getColumnType())),
+                        Map.of("c_varchar_symbol", VARCHAR_COLUMN))
+                .orElseThrow();
+        assertThat(converted.expression()).isEqualTo("(`c_varchar`) IS NOT NULL");
+        assertThat(converted.parameters()).isEqualTo(List.of());
+    }
+
+    @Test
+    public void testConvertNullIf()
+    {
+        // nullif(a_varchar, b_varchar)
+        ParameterizedExpression converted = JDBC_CLIENT.convertPredicate(SESSION,
+                        translateToConnectorExpression(
+                                new NullIfExpression(
+                                        new SymbolReference("a_varchar_symbol"),
+                                        new SymbolReference("b_varchar_symbol")),
+                                ImmutableMap.of("a_varchar_symbol", VARCHAR_COLUMN.getColumnType(), "b_varchar_symbol", VARCHAR_COLUMN.getColumnType())),
+                        ImmutableMap.of("a_varchar_symbol", VARCHAR_COLUMN, "b_varchar_symbol", VARCHAR_COLUMN))
+                .orElseThrow();
+        assertThat(converted.expression()).isEqualTo("NULLIF((`c_varchar`), (`c_varchar`))");
+        assertThat(converted.parameters()).isEqualTo(List.of());
+    }
+
+    private ConnectorExpression translateToConnectorExpression(Expression expression, Map<String, Type> symbolTypes)
+    {
+        return ConnectorExpressionTranslator.translate(
+                        TEST_SESSION,
+                        expression,
+                        TypeProvider.viewOf(symbolTypes.entrySet().stream()
+                                .collect(toImmutableMap(entry -> new Symbol(entry.getKey()), Map.Entry::getValue))),
+                        PLANNER_CONTEXT,
+                        createTestingTypeAnalyzer(PLANNER_CONTEXT))
+                .orElseThrow();
+    }
 }
diff --git a/plugin/trino-mysql/src/test/java/io/trino/plugin/mysql/TestMySqlConnectorTest.java b/plugin/trino-mysql/src/test/java/io/trino/plugin/mysql/TestMySqlConnectorTest.java
index b9929673e15c..1b19e5d699cd 100644
--- a/plugin/trino-mysql/src/test/java/io/trino/plugin/mysql/TestMySqlConnectorTest.java
+++ b/plugin/trino-mysql/src/test/java/io/trino/plugin/mysql/TestMySqlConnectorTest.java
@@ -15,7 +15,13 @@
 
 import com.google.common.collect.ImmutableMap;
 import io.trino.testing.QueryRunner;
+import io.trino.testing.TestingConnectorBehavior;
+import io.trino.testing.sql.TestTable;
+import org.junit.jupiter.api.Test;
 
+import java.util.List;
+
+import static com.google.common.base.Verify.verify;
 import static io.trino.plugin.mysql.MySqlQueryRunner.createMySqlQueryRunner;
 import static org.assertj.core.api.Assertions.assertThat;
 
@@ -30,9 +36,80 @@ protected QueryRunner createQueryRunner()
         return createMySqlQueryRunner(mySqlServer, ImmutableMap.of(), ImmutableMap.of(), REQUIRED_TPCH_TABLES);
     }
 
+    @Override
+    protected boolean hasBehavior(TestingConnectorBehavior connectorBehavior)
+    {
+        return switch (connectorBehavior) {
+            case SUPPORTS_PREDICATE_EXPRESSION_PUSHDOWN -> {
+                // TODO remove once super has this set to true
+                verify(!super.hasBehavior(connectorBehavior));
+                yield true;
+            }
+            default -> super.hasBehavior(connectorBehavior);
+        };
+    }
+
     @Override
     protected void verifyColumnNameLengthFailurePermissible(Throwable e)
     {
         assertThat(e).hasMessageMatching("(Incorrect column name '.*'|Identifier name '.*' is too long)");
     }
+
+    @Test
+    public void testIsNullPredicatePushdown()
+    {
+        assertThat(query("SELECT nationkey FROM nation WHERE name IS NULL")).isFullyPushedDown();
+        assertThat(query("SELECT nationkey FROM nation WHERE name IS NULL OR regionkey = 4")).isFullyPushedDown();
+
+        try (TestTable table = new TestTable(
+                getQueryRunner()::execute,
+                "test_is_null_predicate_pushdown",
+                "(a_int integer, a_varchar varchar(1))",
+                List.of(
+                        "1, 'A'",
+                        "2, 'B'",
+                        "1, NULL",
+                        "2, NULL"))) {
+            assertThat(query("SELECT a_int FROM " + table.getName() + " WHERE a_varchar IS NULL OR a_int = 1")).isFullyPushedDown();
+        }
+    }
+
+    @Test
+    public void testIsNotNullPredicatePushdown()
+    {
+        assertThat(query("SELECT nationkey FROM nation WHERE name IS NOT NULL OR regionkey = 4")).isFullyPushedDown();
+
+        try (TestTable table = new TestTable(
+                getQueryRunner()::execute,
+                "test_is_not_null_predicate_pushdown",
+                "(a_int integer, a_varchar varchar(1))",
+                List.of(
+                        "1, 'A'",
+                        "2, 'B'",
+                        "1, NULL",
+                        "2, NULL"))) {
+            assertThat(query("SELECT a_int FROM " + table.getName() + " WHERE a_varchar IS NOT NULL OR a_int = 1")).isFullyPushedDown();
+        }
+    }
+
+    @Test
+    public void testNullIfPredicatePushdown()
+    {
+        assertThat(query("SELECT nationkey FROM nation WHERE NULLIF(name, 'ALGERIA') IS NULL"))
+                .matches("VALUES BIGINT '0'")
+                .isFullyPushedDown();
+
+        assertThat(query("SELECT name FROM nation WHERE NULLIF(nationkey, 0) IS NULL"))
+                .matches("VALUES CAST('ALGERIA' AS varchar(255))")
+                .isFullyPushedDown();
+
+        assertThat(query("SELECT nationkey FROM nation WHERE NULLIF(name, 'Algeria') IS NULL"))
+                .returnsEmptyResult()
+                .isFullyPushedDown();
+
+        // NULLIF returns the first argument because arguments aren't the same
+        assertThat(query("SELECT nationkey FROM nation WHERE NULLIF(name, 'Name not found') = name"))
+                .matches("SELECT nationkey FROM nation")
+                .isFullyPushedDown();
+    }
 }