AS Core Maths Baseline Assessment

Standard form calculations (Reference: N9)

• Question: Which of the following is the correct standard form of the number 56,000?

• 5.6 x 10^3
• 56 x 10^3
• 560 x 10^2
• 5.6 x 10^4

Answer explanation

In standard form, a number is written as a number between 1 and 10 multiplied by a power of 10. For 56,000, the correct form is 5.6×10^4.

Properties of shapes (Reference: G4)

• Question: Which of the following is a characteristic of all equilateral triangles?

• They have two equal sides.

• They have all angles equal to 60 degrees.

• They have one right angle.

• They have an obtuse angle.

Answer explanation

In an equilateral triangle, all three sides are of equal length, and all three angles are equal to 60 degrees.

Rounding numbers (Reference: N15)

• Question: Round the number 3.14159 to three decimal places: _____

Answer explanation

To round to three decimal places, look at the fourth decimal place (which is 5). Since 5 is 5 or greater, the third decimal place increases by 1, making the number 3.142.

Fractions in ratio problems (Reference: N11)

• Question: The ratio of boys to girls in a class is 3:2. If there are 18 boys, how many girls are there? _____

Answer explanation

The ratio 3:2 means for every 3 boys, there are 2 girls. Set up the proportion 3/2 = 18/x​ and solve for x (girls).

Place value understanding (Reference: N2)

• Question: Explain why place value is important when adding large numbers, such as 7,000 + 300.

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Answer explanation

Place value helps in aligning numbers correctly when performing operations like addition, ensuring accuracy in results.

Algebraic notation (Reference: A4)

• Question: Simplify the expression 2x+3x−5+7

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Answer explanation

Combine the coefficients of like terms 2x+3x to get 5x, and combine constants −5+7 to get 2.

Integer powers and real roots (Reference: N6)

• Question: Calculate the cube root of 64.

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Answer explanation

The cube root of 64 is 4 because 4^3=64.

Substitute numerical values into formulae (Reference: A2)

• Question: Given the formula A=πr^2, find the area of a circle with a radius of 5 cm.

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Answer explanation

Substitute r=5 into the formula A=πr^2, then calculate 5^2=25 and multiply by π to get the area.

Graphs of equations (Reference: A9)

• Question: Plot the graph of the equation y=2x+3 on a coordinate plane provided below.

Answer explanation

For a straight-line equation y=2x+3, plot points like (0,3) and (1,5) by substituting values of x, then connect them with a straight line.

Linear functions (Reference: A12)

• Question: Draw the graph of the function y=−x+2 on the coordinate plane provided.

Answer explanation

The y-intercept is found by setting x=0, and the x-intercept by setting y=0. Plot these points and connect them with a straight line.