Year 10 Revision Workbook 2

Q1.

Simplify fully

...........................................................

(Total for question is 3 marks)

Q2. 

Make x the subject of y =

...........................................................

(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)

...........................................................

(1)

(b)  Factorise     e2 + 4e

...........................................................

(1)

(c)  Solve     7x + 8 = 2x − 3 Show clear algebraic working.

x = ...........................................................

(3)

(d)  Expand and simplify     (y + 10)(y − 2)

...........................................................

(2)

(e)  Factorise fully     20e5f2 − 16e2f

...........................................................

(2)

 

(Total for question = 9 marks)

Q5.Factorise completely (12x − y)2 − (4x − 3y)2

...........................................................

  (Total for Question is 2 marks)

Q6. 

(a)  Factorise 4x2 − 1

...........................................................

(2)

(b)  Solve

Show clear algebraic working.

...........................................................

(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.

...........................................................

(3)(b)  Find the value of P when q = 8

...........................................................

(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.

...........................................................

(Total for question = 3 marks)

Q15. Solve the inequality     5x2 − 13 < 32 Show clear algebraic working.

...........................................................

(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.

...........................................................

 

(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

...........................................................

(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)