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Year 10 Revision Workbook 2
Q1.
Simplify fully
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(Total for question is 3 marks)
Q2.
Make x the subject of y =
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(Total for Question is 4 marks)
Q3.
The diagram shows a circular pond, of radius r metres, surrounded by a circular path. The circular path has a constant width of 1.5 metres.
The area of the path is the area of the pond.
(a) Show that 2r2 − 60r − 45 = 0
(3)
(b) Calculate the area of the pond. Show your working clearly. Give your answer correct to 3 significant figures.
........................................................... m2
(5)
(Total for question = 8 marks)
Q4. (a) Expand 6(4 − 3y)
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(1)
(b) Factorise e2 + 4e
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(1)
(c) Solve 7x + 8 = 2x − 3 Show clear algebraic working.
x = ...........................................................
(3)
(d) Expand and simplify (y + 10)(y − 2)
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(2)
(e) Factorise fully 20e5f2 − 16e2f
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(2)
(Total for question = 9 marks)
Q5.Factorise completely (12x − y)2 − (4x − 3y)2
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(Total for Question is 2 marks)
Q6.
(a) Factorise 4x2 − 1
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(2)
(b) Solve
Show clear algebraic working.
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(4)
(Total for question = 6 marks)
Q7.Prove algebraically that the difference between the squares of any two consecutive odd numbers is always a multiple of 8
(Total for question = 4 marks)
Q8.
(a) Solve
7x + 2y = 16
5x – 2y = 20
Show clear algebraic working.
x = ...........................................................
y = ...........................................................
(3)
(b) Expand and simplify (k + 9)(k – 5)
...........................................................
(2)
(c) Simplify
...........................................................
(3)
(Total for question = 8 marks)
Q9. P is inversely proportional to the square of q. When q = 2, P = 12.8
(a) Find a formula for P in terms of q.
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(3)(b) Find the value of P when q = 8
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(1)
(Total for question = 4 marks)
Q10.
(a) On the grid, draw the graph of y = –2x + 4 for values of x from –1 to 5
(4)(b) Show by shading on the grid, the region defined by all three of the inequalities
y ≤ −2x + 4y ≥ −4x ≥ 1
Label your region R.(3)
(Total for question = 7 marks)
Q11.
The curve C has equation y = x2 – 6x + 4
Using the axes below, sketch the curve C. On your sketch show clearly
(i) the exact coordinates of any points of intersection of C with the coordinate axes,(ii) the coordinates of the turning point.
(Total for question = 6 marks)
Q12.Solve 7x − 5 = 3x + 2 Show your working clearly.
x = ...........................................................
(Total for question is 3 marks)
Q13. (a) Solve the inequalities –4 < 3x + 5 ≤ 11
...........................................................
(3)(b) Write down the integer values of x which satisfy –4 < 3x + 5 ≤ 11
...........................................................
(2)
(Total for question = 5 marks)Q14.
Solve 5x2 + 2x − 4 = 0 Give your solutions correct to 3 significant figures. Show your working clearly.
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(Total for question = 3 marks)
Q15. Solve the inequality 5x2 − 13 < 32 Show clear algebraic working.
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(Total for question = 3 marks)Q16.Solve the simultaneous equations
3x + 4y = 6
5x + 6y = 11
Show clear algebraic working.
x = ...........................................................
y = ...........................................................
(Total for Question is 4 marks)Q17.
Solve x2 + y2 = 20 y = 10 − 2x
Show clear algebraic working.
...........................................................
(Total for question = 5 marks)
Q18. (a) Complete the table of values for y = x2 – 4x + 2
(2)(b) On the grid, draw the graph of y = x2 – 4x + 2 for values of x from –2 to 5
(2)The point P (k, 4) where k > 0 lies on the graph of y = x2 – 4x + 2
(c) Use your graph to find an estimate for the value of k.
...........................................................
(1)
(Total for question = 5 marks)
Q19. The points (1, –1) and (4, 7) lie on the straight line L.
Find an equation for L.
Give your equation in the form ax + by= c where a, b and c are integers.
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(Total for question = 4 marks)Q20. Here is the graph of y = x2 − 2x − 1
(a) Use the graph to solve the equation x2 − 2x − 1 = 2
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(2)The equation x2 + 5x − 7 = 0 can be solved by finding the points of intersection of the line y = ax + b with the graph of y = x2 − 2x − 1
(b) Find the value of a and the value of b.
(2)(Total for question = 4 marks)
Mark SchemeQ1.
Q2.
Q3.
Apart from b, where the mark scheme states otherwise, the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.
Q4.
Apart from c, where the mark scheme states otherwise, the correct answer, unless clearly obtained by an incorrect method, should be taken to imply a correct method.
Q5.
Q6.