Free PERT Exam Questions That Helps Candidates Pass

Point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is slope and (x1,y1)(x_1, y_1) is a point on the line. With m=−23m = -\tfrac{2}{3} and (x1,y1)=(6,1)(x_1, y_1) = (6, 1), substitute directly to get y−1=−23(x−6)y - 1 = -\tfrac{2}{3}(x - 6). That is option A. Option B incorrectly adds signs to both yy and xx, implying a point at (−6,−1)(-6,-1). Option C swaps the roles of xx and yy in the offsets, placing the point at (1,6)(1,6). Option D again reflects wrong signs and coordinates. After establishing point-slope, you can convert to slope-intercept for checking: distribute −23-\tfrac{2}{3}: y−1=−23x+4y - 1 = -\tfrac{2}{3}x + 4. Then add 1: y=−23x+5y = -\tfrac{2}{3}x + 5. Verify by plugging in x=6x=6: y=−23(6)+5=−4+5=1y = -\tfrac{2}{3}(6) + 5 = -4 + 5 = 1, which matches the given point. On PERT, recognizing when point-slope is faster than slope-intercept saves time, especially when a convenient point is provided. The key is sign discipline: y−y1y - y_1 and x−x1x - x_1 must reflect exact coordinates.

In “One of the main reasons…,” the grammatical subject is “One,” which is singular; therefore, the verb must be singular: “is.” Option B correctly pairs “One … is.” Options A and D use plural verbs (“are/were”), and option C also has a singular–plural mismatch in “reason(s).” This construction frequently trips writers because the plural noun “reasons” sits closer to the verb. To avoid errors, identify the true subject before the prepositional phrase “of the main reasons.” In academic writing, subject–verb agreement maintains clarity and professionalism, especially in analytical sentences that front-load complex noun phrases. On PERT, expect agreement checks with “Each,” “Neither,” “One of…,” and collective nouns like “team” or “committee.” A reliable tactic: strip away prepositional phrases and test agreement with the core subject—“One … is.”

Cross-multiplication equates the products of the means and extremes for proportions: 2⋅3=1⋅x2 \cdot 3 = 1 \cdot x. Thus, 6=x6 = x. A quick check confirms: 26=13\frac{2}{6} = \frac{1}{3}. This item gauges comfort with proportions, a core quantitative reasoning skill that appears in scale models, map reading, unit conversions, and rate problems on the PERT. Common errors include inverting the wrong fraction (solving x2=13\frac{x}{2} = \frac{1}{3} by mistake) or attempting to add numerators/denominators. When fractions are simple, an alternative is to reason directly: “Two divided by what equals one-third?” Since 2÷6=132 \div 6 = \tfrac{1}{3}, xx must be 6. In time-pressured settings, cross-multiplying is reliable and fast; just ensure both sides are single fractions and that you have correctly identified the numerators and denominators before multiplying.

When an appositive is nonessential—additional information that can be removed without changing the core meaning—it should be set off with commas on both sides. In “My brother, Alex, is visiting next week,” removing “Alex” leaves “My brother is visiting next week,” which is complete and accurate. Option A treats “Alex” as essential (no commas), implying you have multiple brothers and need the name to specify; that changes meaning. Options C and D use only one comma, yielding punctuation imbalance. PERT Writing expects control over appositives, nonrestrictive clauses, and other interrupters because they affect clarity and tone in academic prose. The reliable test: if the extra information can be omitted without loss of core reference, it’s nonessential—use two commas (or dashes/parentheses as style dictates).

The contrast marker “However” sets up a shift from initial positivity—“impressive” demo—to a cautionary finding—“durability issues” in field tests. This structure supports option C: early promise was tempered by later evidence. Option A contradicts the need to address issues pre-launch. Option B overreaches; the sentence mentions field tests, not lab failure across the board. Option D is the opposite of what’s stated; the demo did not prove long-term reliability. On PERT Reading, recognizing contrast and concession markers (“however,” “although,” “despite”) is crucial to tracking an author’s evolving evaluation. The skill involves weighting evidence: public demos often showcase form and features, while field tests probe endurance and performance. Summarizing that nuanced stance prepares you to handle critical reviews of studies, products, or policies in college work where initial claims meet rigorous validation.