1. The quadratic equation x 2 + kx + 2k – 3 = 0 has no roots. Find the range of values of k.

2. Given p and q are roots of quadratic equation x2 + 3 = k(x + 1), where k is a constant.Find the range of values of k if p and q are two different roots.

3. Given that and are roots of quadratic equation 3x2 + 4x – 6 = 0. Form new quadratic equation whose roots and

4. It is given that 3 and m + 4 are the roots of the quadratic equation x2 + (n – 1)x + 6 = 0 , where m and n are constants. Find the value of m and of n.

(3 marks) / SPM 2012

5. Given a straight line y = mx + 1 is a tangent to the curve x 2 + y2 – 2x + 4y = 0 , where m

is a constant. Find the values of m.

6. Quadratic equation x(3x – p) = 2x – 3, where p is a constant, does not intersects the x-

axis. Find the range of values of p(3 marks) / SBP

2008

7. It is given that quadratic equation x(x – 5) = 4

a. Express the equation in the form of ax2 + bx + c = 0b. State the sum of roots and product of roots of the equationc. Determine the type of roots of the equation.

(4 marks) / SPM 2013

8. The graph of a quadratic function f(x) = px2 – 2x – 3 , where p is a constant, does not intersect the x-axis. Find the range of values of p.

(3 marks) / SPM 2013

HIGH ORDER THINKING SKILL (HOTS)SPM ADDITIONAL MATHEMATICS PAPER 1

HOTS DRILLING EXERCISE

Topic: Quadratic Equations

SPM/SBP Past-Year Questions

ReviewQuestions

1. Given the quadratic equation (1 – a)x2 – 2x + 5 = 0 has no roots, find the range of values

of a.SPM 2014 / 2 marks

2. Given the quadratic equation 2x2 + mx – 5 = 0, where m is a constant, find the value of m if

a. one of the roots of the equation is 2b. the sum of roots of the equation is –4

SPM 2014 / 4 marks

3. In the diagram, the area of the unshaded portion is 72 cm 2. Find the value of x.

HIGH ORDER THINKING SKILL (HOTS)SPM ADDITIONAL MATHEMATICS PAPER 1

HOTS DRILLING EXERCISE

Topic: Quadratic Equations

HOTS (KBAT) Questions and Answer

Forecast Question

s

x cm

x cm

10 cm

8 cm

4. The sum of two numbers is 8. The sum of the squares of the numbers is 34. Find the two numbers.

3. The difference between two numbers is 6 and the product of the numbers is 27. Find the two possible numbers.

4. The diagram shows a trapezium ABCD in which AB = (x – 1) cm, AD = (x + 3) cm and

BC = (3x + 2) cm.

a. Given that the area of the trapezium is 17 cm2 , show that 4x2 + x = 39.

b. Hence, find the value of x.

B

x – 1

x +3

3x +2 C

A D

5. Four squares of which each side is x cm are removed from rectangular metal sheet of

dimensions 20 cm x 15 cm at its corners to form an open box. If the volume of the box is

84x cm3, calculate the value of x.

6. If and are roots of the equation (2x – 1)(x + 5) + k = 0 and , find the value of k.

15 cm

20 cm

x

x

7. Given that the quadratic equation is (3 + m)x2 – (8 + 4m)x + (3 + 4m) = 0. Find the value of

m, if

a. one of the root of the equation is negative of the otherb. one of the root of the equation is reciprocal of the other

8. The roots of quadratic equation x2 + px + q = 0 are k and 3k. Show that 3p2 = 16q

9. Find the range of values of m such that the roots of the equation mx2 – x(x + 4) + 2 = 0

are not real.

10. Given the equation mx2 – 7nx + m = 0 has two equal roots. Find the ratio m : n

11. Diagram shows the answer of a students to solve the equation 2x2 – 3x = 5 by completing

the square. Can you spot the mistake? Correct and complete it.

2x2 – 3x = 5

12. Amir bought x number of T-Shirts for RM 704. He sold 20 of them at a profit of RM 6 each.

a. Write down an expression, in term of x, for the selling price of each T-Shirt.

b. Amir sold the remaining T-Shirts at RM 30 each. Write down, in term of x, the total amount of money he received for all the T-Shirts.

c. Given that Amir received RM 920 altogether, form an equation in x and show that it reduces to 3x2 – 140x + 1408 = 0

d. Solve the equation and hence find the number of T-Shirts Amir bought.

13. Diagram shows the straight line and the curve which can represented by the equations

y = 2x – p and y = x2 – 4 respectively, which intersects at point A and point B. Find the range of values of p.

y = 2x – p

y = x2 – 4A

B

14. Diagram shows the straight line and the curve which can represented by the equations y = 2x – 5 and y = x2 – 2kx + 5k respectively, touches at a point A.Find the values of k.

15. The straight line y = 5x – 1 does not intersect the curve y = 2x2 + x + p. Find the range of values of p

y = x2 – 2kx + 5k

y = 2x – 5

A

y = 2x2 + x + p

y = 5x – 1