Substitution

Algebraic Techniques, SM-Bank 116

Use the algebraic expression \(4-x\) to complete the table. (3 marks)

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(4-x\)

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\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(4-x\)	\(3\)	\(2\)	\(1\)	\(0\)	\(-1\)	\(-6\)

Show Worked Solution

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(4-x\)	\(3\)	\(2\)	\(1\)	\(0\)	\(-1\)	\(-6\)

Algebraic Techniques, SM-Bank 115

Use the algebraic expression \(-x\) to complete the table. (3 marks)

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(-x\)

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\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(-x\)	\(-1\)	\(-2\)	\(-3\)	\(-4\)	\(-5\)	\(-10\)

Show Worked Solution

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(-x\)	\(-1\)	\(-2\)	\(-3\)	\(-4\)	\(-5\)	\(-10\)

Algebraic Techniques, SM-Bank 114

Use the algebraic expression \(5x\) to complete the table. (3 marks)

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(5x\)

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\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(5x\)	\(5\)	\(10\)	\(15\)	\(20\)	\(25\)	\(50\)

Show Worked Solution

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(5x\)	\(5\)	\(10\)	\(15\)	\(20\)	\(25\)	\(50\)

Algebraic Techniques, SM-Bank 113

Use the algebraic expression \(x^2-3x\) to complete the table. (3 marks)

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(x^2-3x\)

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\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(x^2-3x\)	\(-2\)	\(-2\)	\(0\)	\(4\)	\(10\)	\(70\)

Show Worked Solution

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(x^2-3x\)	\(-2\)	\(-2\)	\(0\)	\(4\)	\(10\)	\(70\)

Algebraic Techniques, SM-Bank 112

Use the algebraic expression \(x^2+1\) to complete the table. (3 marks)

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(x^2+1\)

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\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(x^2+1\)	\(2\)	\(5\)	\(10\)	\(17\)	\(26\)	\(101\)

Show Worked Solution

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(x^2+1\)	\(2\)	\(5\)	\(10\)	\(17\)	\(26\)	\(101\)

Algebraic Techniques, SM-Bank 111

Use the algebraic expression \(2x+1\) to complete the table. (3 marks)

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(2x+1\)

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\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(2x+1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(21\)

Show Worked Solution

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(2x+1\)	\(3\)	\(5\)	\(7\)	\(9\)	\(11\)	\(21\)

Algebraic Techniques, SM-Bank 110

Use the algebraic expression \(x-5\) to complete the table. (3 marks)

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(x-5\)

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\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(x-5\)	\(-4\)	\(-3\)	\(-2\)	\(-1\)	\(0\)	\(5\)

Show Worked Solution

\(x\)	\(1\)	\(2\)	\(3\)	\(4\)	\(5\)	\(10\)
\(x-5\)	\(-4\)	\(-3\)	\(-2\)	\(-1\)	\(0\)	\(5\)

Algebraic Techniques, SM-Bank 109

Use the algebraic expression \(x+3\) to complete the table. (3 marks)

\(x\)	1	2	3	4	5	10
\(x+3\)

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\(x\)	1	2	3	4	5	10
\(x+3\)	4	5	6	7	8	13

Show Worked Solution

\(x\)	1	2	3	4	5	10
\(x+3\)	4	5	6	7	8	13

Algebraic Techniques, SM-Bank 044

Evaluate the expression \(x^2+3x-4\) when:

\(x=1\) (2 marks)

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\(x=3\) (2 marks)

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a. \(0\)

b. \(14\)

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a.	\(x^2+3x-4\)	\(=1^2+3\times 1-4 \)
		\(=1\times 1 +3-4\)
		\(=0\)

b.	\(x^2+3x-4\)	\(=3^2+3\times 3-4\)
		\(=3\times 3 +3\times 3-4\)
		\(=14\)

Algebraic Techniques, SM-Bank 043

Evaluate the expression \(-2x^2\) when:

\(x=1\) (1 mark)

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\(x=-2\) (2 marks)

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\(x=-\dfrac{1}{2}\) (2 marks)

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a. \(-2\)

b. \(-8\)

c. \(-\dfrac{1}{2}\)

Show Worked Solution

a.	\(-2x^2\)	\(=-2\times 1^2\)
		\(=-2\times 1\times 1\)
		\(=-2\)

b.	\(-2x^2\)	\(=-2\times (-2)^2\)
		\(=-2\times (-2)\times (-2)\)
		\(=-8\)

c.	\(-2x^2\)	\(=-2\times \bigg(-\dfrac{1}{2}\bigg)^2\)
		\(=-2\times \bigg(-\dfrac{1}{2}\bigg) \times \bigg(-\dfrac{1}{2}\bigg)\)
		\(=-2\times\dfrac{1}{4}\)
		\(=-\dfrac{1}{2}\)

Algebraic Techniques, SM-Bank 042

Evaluate the expression \(w^2\) when:

\(w=4\) (1 mark)

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\(w=-1\) (2 marks)

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\(w=\dfrac{1}{3}\) (2 marks)

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a. \(16\)

b. \(1\)

c. \(\dfrac{1}{9}\)

Show Worked Solution

a.	\(w^2\)	\(=4^2\)
		\(=4\times 4\)
		\(=16\)

b.	\(w^2\)	\(=(-1)^2\)
		\(=(-1)\times (-1)\)
		\(=1\)

c.	\(w^2\)	\(=\bigg(\dfrac{1}{3}\bigg)^2\)
		\(=\dfrac{1}{3}\times \dfrac{1}{3}\)
		\(=\dfrac{1}{9}\)

Algebraic Techniques, SM-Bank 041

Evaluate the expression \(\dfrac{c}{2}-\dfrac{b}{3}+a\) when \(a=-4\), \(b=-3\) and \(c=10\). (2 marks)

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\(2\)

Show Worked Solution

\(\dfrac{c}{2}-\dfrac{b}{3}+a\)	\(=\dfrac{10}{2}-\bigg(\dfrac{-3}{3}\bigg)+(-4)\)
	\(=5-(-1)-4\)
	\(=2\)

Algebraic Techniques, SM-Bank 040

Evaluate the expression \(\dfrac{20}{c}+\dfrac{15}{d}\) when \(c=-2\) and \(d=3\). (2 marks)

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\(-5\)

Show Worked Solution

\(\dfrac{20}{c}+\dfrac{15}{d}\)	\(=\dfrac{20}{-2}+\dfrac{15}{3}\)
	\(=-10+5\)
	\(=-5\)

Algebraic Techniques, SM-Bank 039

Evaluate the expression \(11+a-3b\) when \(a=13\) and \(b=8\). (2 marks)

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\(0\)

Show Worked Solution

\(11+a-3b\)	\(=11+13-3\times 8\)
	\(=11+13-24\)
	\(=0\)

Algebraic Techniques, SM-Bank 038

Evaluate the expression \(-2x+7y\) when \(x=1\) and \(y=-2\). (2 marks)

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\(-16\)

Show Worked Solution

\(-2x+7y\)	\(=-2\times 1+7\times -2\)
	\(=-2-14\)
	\(=-16\)

Algebraic Techniques, SM-Bank 037

Evaluate the expression \(4m-5n\) when \(m=2\) and \(n=4\). (2 marks)

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\(-12\)

Show Worked Solution

\(4m-5n\)	\(=4\times 2-5\times 4\)
	\(=8-20\)
	\(=-12\)

Algebraic Techniques, SM-Bank 036

Evaluate the expression \(3z+11\) when \(z=3\). (1 mark)

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\(20\)

Show Worked Solution

\(3z+11\)	\(=3\times 3+11\)
	\(=9+11\)
	\(=20\)

Algebraic Techniques, SM-Bank 035

Evaluate the expression \(-2-5m\) when \(m=-1\). (1 mark)

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\(3\)

Show Worked Solution

\(-2-5m\)	\(=-2-5\times (-1)\)
	\(=-2+5\)
	\(=3\)

Algebraic Techniques, SM-Bank 034

Evaluate the expression \(10-2y\) when \(y=4\). (1 mark)

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\(2\)

Show Worked Solution

\(10-2y\)	\(=10-2\times 4\)
	\(=10-8\)
	\(=2\)

Algebraic Techniques, SM-Bank 033 MC

When \(\large x\)\(=5\) and \(\large y\)\(=-2\) the value of the expression \(2x+3y\) is:

\(4\)
\(8\)
\(16\)
\(-7\)

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\(A\)

Show Worked Solution

\(2x+3y\)	\(=2\times 5+3\times -2\)
	\(=10+-6\)
	\(=4\)

\(\Rightarrow A\)

Algebraic Techniques, SM-Bank 032 MC

When \(\large a\)\(=2\) and \(\large b\)\(=-1\) the value of the expression \(a+b\) is:

\(-21\)
\(-2\)
\(-1\)
\(1\)

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\(D\)

Show Worked Solution

\(a+b\)	\(=2+-1\)
	\(=1\)

\(\Rightarrow D\)

Algebraic Techniques, SM-Bank 031 MC

When \(x=4\) the value of the expression \(3\times x\) is:

\(34\)
\(7\)
\(12\)
\(12x\)

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\(C\)

Show Worked Solution

\(3\times x\)	\(=3\times 4\)
	\(=12\)

\(\Rightarrow C\)