SAT Math Practice Problems
1.If f(x)=3x−4f(x) = 3x – 4f(x)=3x−4 and g(x)=2x+1g(x) = 2x + 1g(x)=2x+1, what is the value of 4f(3)−g(5)4f(3) – g(5)4f(3)−g(5)?A) 14
B) 15
C) 17
D) 19
Solution:
First, let’s find f(3)f(3)f(3) and g(5)g(5)g(5): f(3)=3(3)−4=9−4=5f(3) = 3(3) – 4 = 9 – 4 = 5f(3)=3(3)−4=9−4=5g(5)=2(5)+1=10+1=11g(5) = 2(5) + 1 = 10 + 1 = 11g(5)=2(5)+1=10+1=11
Now, substitute these values into the expression 4f(3)−g(5)4f(3) – g(5)4f(3)−g(5): 4f(3)−g(5)=4(5)−11=20−11=94f(3) – g(5) = 4(5) – 11 = 20 – 11 = 94f(3)−g(5)=4(5)−11=20−11=9
Therefore, the correct answer is:
A) 9
2. If f(x)=x2−2x+1f(x) = x^2 – 2x + 1f(x)=x2−2x+1 and g(x)=x+3g(x) = x + 3g(x)=x+3, what is the value of f(4)+2g(2)f(4) + 2g(2)f(4)+2g(2)?A) 21
B) 23
C) 25
D) 27
Solution:
First, let’s find f(4)f(4)f(4) and g(2)g(2)g(2): f(4)=42−2(4)+1=16−8+1=9f(4) = 4^2 – 2(4) + 1 = 16 – 8 + 1 = 9f(4)=42−2(4)+1=16−8+1=9g(2)=2+3=5g(2) = 2 + 3 = 5g(2)=2+3=5
Now, substitute these values into the expression f(4)+2g(2)f(4) + 2g(2)f(4)+2g(2): f(4)+2g(2)=9+2(5)=9+10=19f(4) + 2g(2) = 9 + 2(5) = 9 + 10 = 19f(4)+2g(2)=9+2(5)=9+10=19
Therefore, the correct answer is:
D) 19
3. If f(x)=2×2+3xf(x) = 2x^2 + 3xf(x)=2×2+3x and g(x)=x−1g(x) = x – 1g(x)=x−1, what is the value of f(1)−g(3)f(1) – g(3)f(1)−g(3)?A) 4
B) 5
C) 6
D) 7
Solution:
First, let’s find f(1)f(1)f(1) and g(3)g(3)g(3): f(1)=2(1)2+3(1)=2+3=5f(1) = 2(1)^2 + 3(1) = 2 + 3 = 5f(1)=2(1)2+3(1)=2+3=5g(3)=3−1=2g(3) = 3 – 1 = 2g(3)=3−1=2
Now, substitute these values into the expression f(1)−g(3)f(1) – g(3)f(1)−g(3): f(1)−g(3)=5−2=3f(1) – g(3) = 5 – 2 = 3f(1)−g(3)=5−2=3
Therefore, the correct answer is:
A) 3
4. If f(x)=x3−xf(x) = x^3 – xf(x)=x3−x and g(x)=2x+4g(x) = 2x + 4g(x)=2x+4, what is the value of 2f(2)+g(1)2f(2) + g(1)2f(2)+g(1)?A) 16
B) 18
C) 20
D) 22
Solution:
First, let’s find f(2)f(2)f(2) and g(1)g(1)g(1): f(2)=23−2=8−2=6f(2) = 2^3 – 2 = 8 – 2 = 6f(2)=23−2=8−2=6g(1)=2(1)+4=2+4=6g(1) = 2(1) + 4 = 2 + 4 = 6g(1)=2(1)+4=2+4=6
Now, substitute these values into the expression 2f(2)+g(1)2f(2) + g(1)2f(2)+g(1): 2f(2)+g(1)=2(6)+6=12+6=182f(2) + g(1) = 2(6) + 6 = 12 + 6 = 182f(2)+g(1)=2(6)+6=12+6=18
Therefore, the correct answer is:
B) 18
5. If f(x)=4x−1f(x) = 4x – 1f(x)=4x−1 and g(x)=x2+xg(x) = x^2 + xg(x)=x2+x, what is the value of 3f(3)−g(2)3f(3) – g(2)3f(3)−g(2)?A) 19
B) 20
C) 21
D) 22
Solution:
First, let’s find f(3)f(3)f(3) and g(2)g(2)g(2): f(3)=4(3)−1=12−1=11f(3) = 4(3) – 1 = 12 – 1 = 11f(3)=4(3)−1=12−1=11g(2)=22+2=4+2=6g(2) = 2^2 + 2 = 4 + 2 = 6g(2)=22+2=4+2=6
Now, substitute these values into the expression 3f(3)−g(2)3f(3) – g(2)3f(3)−g(2): 3f(3)−g(2)=3(11)−6=33−6=273f(3) – g(2) = 3(11) – 6 = 33 – 6 = 273f(3)−g(2)=3(11)−6=33−6=27
Therefore, the correct answer is:
C) 27
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