Topic 2 Algebra 1 Flashcards
Algebra Revision
What is substitution in algebra?
Substitution is the process of replacing a variable with a number or another expression.
True or False: Substitution can only be used in equations, not in expressions.
False
Solve 7 - 3a = 1
-3a = 1 - 7
a = -6/-3
a = 2
Expand (x+3)(x-2)
x^2 -2x + 3x -6
Simplify to give
x^2 + x - 6
If x = 3, what is the value of 2x + 5?
11
Solve x + 4 = 3x + 9
x - 3x = 9 - 4
-2x = 5
x = - 5/2
What is the result of substituting x = -1 in the equation x^2 + 3x?
2
If m = 1 and n = m^2 + 3, what is the value of n?
4
Fill in the blank: The expression 4y + 2 when y = 5 equals _____.
22
Simplify 5g - 3h - 7g + 6h
-2g + 3h
If p = 6 and q = 2p - 4, what is the value of q?
8
Multiple Choice: If x = 3, what is the value of the expression 4(x + 1)? A) 8 B) 12 C) 16 D) 20
B) 16
True or False: Substituting a variable can change the solution of an equation.
False
Multiple Choice: Which of the following is a correct substitution for x in the expression 5x + 2 when x = 4? A) 20 B) 14 C) 18 D) 22
D) 22
Fill in the blank: In the expression 7x + 2 when x = 0, the result is _____.
2
Solve
2a - b = 6 and
2a + 3b = -6
Subtract eq. 2 from eq. 1 gives:
-4b = 12
b = -3. Substitute b = -3 into eq. 1 gives a = 1 1/2
Expand and simplify
(x-2)(x-3)(x-4)
Expand 2 brackets first
(x-2)[(x-3)(x-4)]
= (x-2)[x^2 - 7x +12]
Expand again.
= x^3 - 7x^2 + 12x - 2x^2 + 14x - 24
Simplify
= x^3 - 9 x^2 + 26x - 24
Simplify a - 2b - 3a + 7b
-2a + 5b
True or False: In substitution, you can replace a variable with any expression.
True
Expand x(x -4)
x^2 - 4x
Expand (2x - 3)^3
Write out in full.
(2x - 3)[(2x - 3)(2x - 3)]
Expand square brackets first.
= (2x - 3)[4x^2 - 12x + 3]
Expand again
= 8x^3 - 24x^2 + 18x - 12x^2 + 36x -27
Simplify
8x^3 - 36x^2 +54x - 27
If a = 2 and b = a^3 + 1, what is the value of b?
9
Solve
x + 2y = 5 and
x - y = 8
Use elimination. Subtract eq. 2 from eq. 1.
3y = -3 so y = -1. Substitute y = -1 into eq. 2 we get
x - -1 = 8, x + 1 = 8, x =7.
