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SAT Math Practice: Fundamentals Practice

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SAT Math Practice: Fundamentals Practice

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Medium-level practice on core algebra topics

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Eman Gamal
Eman Gamal
Egypt

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SAT Math Practice: Fundamentals Practice
 

SAT Math Practice: Fundamentals PracticeOnline version

Medium-level practice on core algebra topics

by Eman Gamal
1

1. Solve the radical equation: sqrt(x+4) = 3. What is x?

2

2. Solve the rational equation: 18/(r+10) = 3/r. What is r?

3

3. Which value is extraneous for sqrt(t+4) = t-2?

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4. Solve using quadratic formula: x = (-b ± sqrt(b^2-4ac))/(2a) with a=1,b=-3,c=2. Roots?

5

5. Which statement is true about discriminant D=b^2-4ac?

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6. If a quadratic has D=0, how many real solutions does it have?

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7. Solve for x: x^2 -5x = 0.

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8. Factor and solve: x^2+5x+6=0.

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9. Which expression is equivalent to 4x^2+12x+9 after factoring?

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10. Absolute value inequality: |x-2| ≤ 3. Domain of x is?

Feedback

Square both sides: x+4=9 → x=5.

Cross-multiply: 18r = 3(r+10) → 18r=3r+30 → 15r=30 → r=2.

Squaring gives t(t-5)=0; t=0 is extraneous since 2 ≠ 0.

Discriminant 9-8=1; roots (3±1)/2 → 2 and 1.

D>0 yields two real roots; D=0 one real; D<0 no real.

Discriminant zero gives a repeated real root.

Factor: x(x-5)=0 → x=0 or x=5.

Factoring (x+2)(x+3)=0 so x=-2,-3.

Recognize as (2x)^2+2·2x·3+3^2.

Distance from 2 is at most 3: -1 ≤ x ≤ 5.

 
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