SATs Year 6 Level Mathematics

Solve the quadratic equation: 2x^2 + 5x - 3 = 0

• x = 1, -2

• x = -4, 1

• x = 3, -1

• x = 0.5, -3

Answer explanation

To solve the quadratic equation 2x^2 + 5x - 3 = 0, factor the equation to (2x - 1)(x + 3) = 0. Set each factor to zero to find x = 0.5, -3.

Calculate the value of y when x = 2 in the exponential function y = 3 * 2^x

• 6

• 8

• 10

• 12

Answer explanation

Substitute x = 2 into the function y = 3 * 2^x to get y = 3 * 2^2 = 3 * 4 = 12. Therefore, when x = 2, y = 12.

Find the sine of an angle of 30 degrees in trigonometry

• 0.25

• 0.75

• 0.5

• 1.0

Answer explanation

The sine of a 30-degree angle in trigonometry is 0.5. Therefore, the correct answer is 0.5.

Determine the slope of the line passing through the points (2, 3) and (5, 7)

• 1/2

• 2/3

• 5/4

• 4/3

Answer explanation

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). Substituting the values, we get (7 - 3) / (5 - 2) = 4 / 3, which is the correct slope.

What is the mean of the following data set: 5, 8, 12, 15, 20

• 12

• 10

• 25

• 18

Answer explanation

The mean is calculated by adding all numbers together and dividing by the total count. (5+8+12+15+20)/5 = 60/5 = 12. Therefore, the mean of the data set is 12.

Calculate the area of a triangle with base 6 cm and height 4 cm

• 24 square cm

• 12 square cm

• 10 square cm

• 8 square cm

Answer explanation

To calculate the area of a triangle, use the formula: Area = 0.5 * base * height. Substituting the values, Area = 0.5 * 6 cm * 4 cm = 12 square cm. Therefore, the correct answer is 12 square cm.

A word problem: If John has 3 apples and gives 1 to each of his 2 friends, how many apples does he have left?

• 0

• 2

• 1

• 4

Answer explanation

After giving 2 apples to his friends, John will have 1 apple left. Therefore, the correct answer is 1.

Solve the equation: 3x + 5 < 2x - 1

• x < -5

• x > -6

• x = -6

• x < -6

Answer explanation

Subtract 2x from both sides to get x + 5 < -1. Then subtract 5 from both sides to get x < -6. Therefore, the correct answer is x < -6.

What is the value of sin(45 degrees) in trigonometry?

• 1/2

• 1

• sqrt(2)/2

• 0

• -1

Answer explanation

The value of sin(45 degrees) in trigonometry is sqrt(2)/2, which represents the ratio of the length of the side opposite the angle to the hypotenuse in a right triangle with a 45-degree angle.

If a rectangle has a length of 8 cm and a width of 4 cm, what is its perimeter?

• 12 cm

• 24 cm

• 16 cm

• 32 cm

Answer explanation

To find the perimeter of a rectangle, you add up all the sides. In this case, 8 cm + 8 cm + 4 cm + 4 cm = 24 cm. Therefore, the correct answer is 24 cm.