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Mathematics for IGCSE & O level - Equations (Section 1)

1
What are the coordinates of the x-intercept of the line y = 2x - 6?
Answer
(B)
(3, 0)
2
When solving a quadratic equation, when would you use the completing the square method?
Answer
(C)
To rewrite the equation in a perfect square form.
3
What type of solution is obtained when solving a quadratic equation by completing the square?
Answer
(D)
All of the above.
4
Which methods are typically employed for solving quadratic equations?
Answer
A
B
C
5
What is a common application of the quadratic formula?
Answer
(B)
Solving for roots in a quadratic equation.
6
If a = 3 and b = 2, what is the value of a + 2b?
Answer
(B)
7
7
Which step comes first when changing the subject of a formula if there are parentheses?
Answer
(B)
Distribute the terms within the parentheses.
8
What must be done after applying a transformation to one side of an equation to maintain equality?
Answer
(A)
Do the same operation to the other side.
9
Solve the system of equations: 3x + y = 4; 2x - y = 6.
Answer
(A)
x=2, y=-2
10
What is the common error in the sign when the order is a subtraction?
Answer
(A)
Distribute incorrectly
11
What mathematical operation is used to get rid of a square?
Answer
(D)
Taking the square root
12
If a = 20 and b = 17, what is the value of a-b?
Answer
(B)
3
13
When solving the equation x² - 4x + 4 = 0, what should you do?
Answer
A
B
C
14
If x/2 + 4 = 10, then what is the value of x?
Answer
(B)
12
15
Solve: x/2 + x/3 = 5
Answer
(B)
8
16
What does it mean when the coefficient of x² is '1'?
Answer
(C)
The equation can be solved easily.
17
If the base of a triangle is 'b' and its height is 'h', what is the formula for the area 'A' of the triangle?
Answer
(B)
A = 1/2*b*h
18
Which methods are typically used to solve quadratic equations?
Answer
A
B
C
19
Simplify: 4x + 2(x - 1)
Answer
(A)
6x - 2
20
What is the solution to 3(x - 1) = 9?
Answer
(B)
4
21
What does 'P' usually represent in the context of geometric shapes?
Answer
(B)
Perimeter
22
What value of x satisfies the equation 4x + 2 = 10?
Answer
(A)
4
23
What are the possible number of solutions to a quadratic equation?
Answer
(C)
Zero, one, or two
24
What is the first step when changing the subject of a formula?
Answer
(B)
Simplify and collect terms
25
Which method(s) can be used to solve simultaneous equations?
Answer
A
B
C
26
If x - 6 = 10, then x equals?
Answer
(A)
16
27
What is the purpose of setting each factor to zero after factoring a quadratic equation?
Answer
(B)
To find the roots of the equation.
28
Which of the following is a main source of error when using the quadratic formula?
Answer
(D)
Incorrectly identifying the coefficients a, b, and c.
29
What do you do after you factorize a quadratic equation?
Answer
B
C
30
The sum of two numbers is 10, and their difference is 4. Write a system of equations to solve this.
Answer
(A)
x + y = 10, x - y = 4
31
What does it mean to 'isolate' a variable?
Answer
(A)
To get the variable by itself on one side of the equation.
32
Which formulas are commonly used to help solve quadratic equations?
Answer
A
B
C
33
The formula for the area of a triangle is A = 1/2 * b * h. If b=6 and h=4, what is A?
Answer
(C)
12
34
When is it essential to give your answer correct to a certain number of decimal places?
Answer
(C)
When the question specifically asks for it.
35
What does the 'a' variable represent in the formula for the area of a rectangle?
Answer
(C)
Area
36
Solve for the equation x+3/2=5, and determine which of these is the correct solution.
Answer
(B)
x=7/2
37
If the diameter of a circle is 10 cm, what is the radius?
Answer
(A)
5 cm
38
If a rectangle has a length of 8cm and a width of 4cm, what is its area?
Answer
(A)
32 cm^2
39
What is the advantage of completing the square?
Answer
(B)
It transforms the equation into a form that is easily solvable.
40
If x = 5 and y = 2, what is the value of 3x - 2y?
Answer
(B)
2
41
Solve: 2(x + 1) = 8
Answer
(C)
3
42
In which form can a quadratic expression be written after completing the square?
Answer
(A)
(x + p)² + q
43
Given the equation A=1/2bh. Solve for b?
Answer
(A)
b=2A/h
44
What is the formula to calculate the perimeter of a rectangle?
Answer
(B)
2l + 2w
45
What is the first step in simplifying an expression with a bracket?
Answer
(C)
Expand the bracket
46
What is the area of a circle whose radius is 7 units?
Answer
(B)
49 π
47
When completing the square, what needs to be added to x² + bx to complete the square?
Answer
(A)
(b/2)²
48
What is the value of x if 2x + 3 = 9?
Answer
(A)
3
49
If the selling price, S, of an item is the cost, C, plus a markup of M, which equation represents this relationship?
Answer
(A)
S = M + C
50
What is the value of x, in the following equation: 6x - 10 = 2x + 2?
Answer
(A)
3