# Study Guide

## MoGEA Mathematics SubtestSample Questions

### Competency 0006Understand numbers and algebra.

1. At a community plant sale, a gardener buys 60 plants. Some cost \$5 per plant and the rest cost \$3 per plant. The total cost of the plants is \$236. If x represents the number of \$3 plants, which of the following equations could be solved to find the number of \$3 plants purchased?

1. 3x + 5(60 - x) – 236 = 0
2. 5x + 3(60 – x) – 236 = 0
3. 3x + 5(x – 60) – 236 = 0
4. 5x + 3(x – 60) – 236 = 0
Correct Response: A. This question requires the examinee to represent and solve real-world problems using algebraic expressions and equations. If the gardener purchased x plants that cost \$3 each and 60 plants altogether, then the gardener purchased 60 – x plants that cost \$5 each. The value of the \$3 plants is 3x and the value of the \$5 plants is 5(60 – x). As the total value of the purchase was \$236, the equation that could be solved to find the number of \$3 plants purchased is 3x + 5(60 – x) = 236, or 3x + 5(60 – x) – 236 = 0.

### Competency 0007Understand measurement and geometry.

2. Use the incomplete geometric proof below to answer the question that follows.

 Given: ABCD is a parallelogramAW ≅ XC Prove: WY ≅ YX Statements ABCD is a parallelogram. AW ≅ XC AB || DC ∠WAC ≅ ∠XCA∠AWX ≅ ∠CXW ΔAWY ≅ ΔCXY WY ≅ YX Reasons Given Given Definition of a parallelogram If parallel lines are crossed by a transversal, alternate interior angles are congruent. ? Corresponding parts of congruent triangles are congruent.

Which of the following is the reason for Statement 5 in the proof above?

1. AAS
2. AAA
3. ASA
4. SAS