Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 2
105 practice questions
Topics covered
Practice questions
1–10 of 19 · Hard
Question 1
5 marks · Hard
Answer and see the solution →The distance from the Earth to Star X is 2.46 × 10^{12} km. The distance from the Earth to Star Y is 7.82 × 10^{13} km.
(a)[3 marks]Calculate how many times farther Star Y is from Earth compared to Star X. Give your answer in standard form.
(b)[2 marks]If a spaceship travels at 2.05 × 10^{5} km per hour, estimate how many hours it would take to reach Star X from Earth. Give your answer in standard form.
Question 2
4 marks · Hard
Answer and see the solution →Evaluate (4.8 \times 10^{-3}) \times (6.2 \times 10^{5}) and give your answer in standard form.
Question 3
6 marks · Hard
Answer and see the solution →A laboratory measures the masses of three specimens. Their masses are given below:
Specimen Mass (g) A 0.00741 B 0.0741 C 0.00417 (a)[3 marks]Write the mass of each specimen in standard form.
(b)[1 mark]Arrange the specimens in order of increasing mass.
(c)[2 marks]Calculate the difference in mass between specimen B and specimen C. Give your answer in standard form.
Question 4
4 marks · Hard
Answer and see the solution →Consider the following expression:
Simplify the expression as much as possible, giving your answer in terms of a single fraction.
(a)[2 marks]Simplify and write your answer as a single fraction.
(b)[1 mark]Simplify and write your answer as a single fraction.
(c)[1 mark]Hence or otherwise, simplify the entire expression completely.
Question 5
5 marks · Hard
Answer and see the solution →The formula for the area of a parallelogram is , where is the base and is the height.
(a)[2 marks]Given , , express the area in terms of using index notation.
(b)[3 marks]If , solve for . Give all possible positive values for .
Question 6
3 marks · Hard
Answer and see the solution →Given the formula , rearrange this formula to make the subject. Show all steps clearly.
Question 7
5 marks · Hard
Answer and see the solution →Let , , and be positive numbers. Given that can be written as , find the values of , , and . Show all your working.
(a)[1 mark]Expand and simplify .
(b)[1 mark]Expand and simplify .
(c)[3 marks]Simplify the entire expression by dividing your answers to parts (a) and (b).
Question 8
6 marks · Hard
Answer and see the solution →The line L passes through P (–4, 5) and Q (2, –1). A second line M is parallel to L and passes through the point R (1, 7).
(a)[3 marks]Find the equation of the line L in the form y = mx + c.
(b)[1 mark]Write down the gradient of line M.
(c)[2 marks]Find the equation of line M in the form y = mx + c.
Question 9
5 marks · Hard
Answer and see the solution →The lines y = 2x + 3 and y = -x + k intersect at the point (1, 5).
(a)[2 marks]Find the value of k.
(b)[2 marks]Verify that (1, 5) lies on both lines.
(c)[1 mark]Determine the equation of the line that passes through the origin and the point of intersection.
Question 10
4 marks · Hard
Answer and see the solution →In the diagram below, ABCD is a cyclic quadrilateral inside a circle with centre O.
Cyclic quadrilateral with angles marked. Angle BAD = 82° and angle BCD = 71°.
Calculate the size of angle ABC, giving a reason for each step of your working.