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THE PERSONAL TEST PREP EVERYTHING HANDOUT
ENGLISH
#1 REASON STUDENTS DON’T GET THE SCORE THEY DESERVE: CARELESSNESS.
SOLUTION: SLOW DOWN.
FILL IN THE BLANK QUESTIONS: Read each choice with expression from the first word of the sentence to the last.
After completing a paragraph, re-read it with all of your choices.
WHICH CHOICE QUESTIONS: Underline the important part of the question. Pay attention to the word specific.
RULES
SEMICOLONS connect independent clauses, two parts that could be complete sentences on their own.
No: I love cheese, my favorite is Swiss. Yes: I love cheese; my favorite is Swiss. Semicolons also separate items in a list
when some items contain commas. They sold oranges, when in season; apples, grown locally; and mangoes.
COMMAS: Say the sentence with/without a long pause where the comma is. Is the pause really needed there?
A pair of commas around an interrupting phrase is often correct: The guitar, now that it was tuned, sounded great.
COLONS set off lists or explanations after an independent clause. After a colon, either kind of clause is fine.
The colon is NOT ONLY FOR LISTS! She wanted one thing: victory.
PRONOUNS: To choose the right pronoun, find the noun it replaces. Singular pronouns replace singular nouns.
No: The seniors at school took finals before they closed for the holidays. Yes: . . . it closed, since school is singular.
“Which” follows a comma and refers to the word right before the comma. The test, which I took Saturday, went very well.
MODIFIERS: If one part of a sentence modifies (is about) another part, get the parts right next to each other.
No: While on vacation, the books Lulu read were mysteries. Yes: While on vacation, Lulu read mysteries. (“While on
vacation” is the modifying phrase. It is modifying “Lulu.”) Modifying phrases often start sentences, and are then followed by a
comma. Before going outside, the cat looked into the yard. (“Before going outside” is the modifying phrase. It modifies “cat.”)
SUBJECT/VERB AGREEMENT. Don’t assume that the word just before the verb is the subject of that verb.
No: The movement of the snakes are beautiful and strange. Yes: The movement . . . is beautiful and strange.
(“Movement” – the subject – is singular and agrees with the singular verb “is.”)
REDUNDANCY: 1 or 2-word choices are often correct because all other choices are redundant.
READING: Practice timed! 9 minutes, then 8, 7, 6.
SKREADING: (60 to 90 seconds)
READ the intro.
READ enough of the 1st paragraph to get its main idea.
READ the first 1 or 2 sentences of the other paragraphs.
READ the last sentence of a paragraph if the first sentence of the next paragraph is unclear.
SKIM the rest of the passage for sentences that begin with But, However, Although, etc.
Stuck? Review the skread sentences.
SCIENCE: Practice timed! 6 minutes, then 5, 4, 3.
ANALYSIS: (30 to 60 seconds)
READ the 1 sentence or two.
READ the sentence immediately before the description of an Experiment or Study.
STUDY the figures. Note trends in the data and differences between similar figures.
READ more text if a question requires that you do so.
Stuck? Read the answers for clues.
st
For the Conflicting Viewpoints passage, read the 1st sentence, the sentence immediately before the viewpoints, and then a little
of each viewpoint.
MATH
REMEMBER! Figures are drawn to scale.
REMEMBER! Don’t choose simple answers to hard questions.
AREA: Parallelogram = bh. Triangle = bh/2. Trapezoid = (average of bases) x h
VOLUME: Rectangular solid = LWH. Cylinder (can) = πr h.
CIRCLE: Area = πr Circumference = πd.
Rectangular prism: Diag = L + W + H . For any shape: (# of sides – 2) x 180 = total degrees.
If two parallel lines are cut by a 3 line, this creates four small (equal) angles and four big (equal) angles.
2
2
2
2
2
2
rd
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Memorize the 3 Special Right Triangles below.
If the legs of a triangle are each 7, the hypotenuse is 7√2. (Triangle 1)
If the legs of a triangle are 5 and 5√3 the hypotenuse is 10. (Triangle 2)
If the legs of a triangle are 60 and 80, the hypotenuse is 100. (Triangle 3)
Special Triangle #1
x
x√2
45°
x
Special Triangle #2
2x
60°
Special Triangle #3
3x
Similar Triangles
5x
A
4x
C E
D
30°
45°
x
x√3
B
Similar triangles, like ABC and DBE above, have the same angles. Their sides have the same proportions (ratios).
Right triangles can be used to find the distance between two points. Connect the two points and make that line segment into
the hypotenuse of a triangle. Now use a + b = c (or you may have created one of the Special Triangles).
2
2
2
Any triangle: The length of a side must be less than the sum and greater than the difference of the other two sides.
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GRAPHS: Line: y = mx + b. Slope = rise/run. Perpendicular lines have opposite reciprocal slopes.
Circle: (x – h) + (y – k) = r , where (h,k) is the center point. Parabola: y = x . y = x + 1 shifts it up. y = (x – 1) shifts it
right. y = -x flips it downwards. y = 2x narrows it.
The midpoint of two points is the average of their coordinates.
2
2
2
2
2
2
2
2
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SOH CAH TOA: Sine of an angle = opposite side over hypotenuse. Cosine = adjacent over hypotenuse. Tangent = opposite
over adjacent.
Reciprocals: sine/cosecant cosine/secant tangent/cotangent.
2
Trig Rules: sin x + cos2x = 1;
sin/cos = tan;
If sin x = cos y, then x + y = 90;
Since sin 30° = ½ . . . sin-1 (½) = 30°
An angle can be measured using radians. 180° = π radians.
In the figure to the right, A = All, S = sine, etc. So, for example, if an angle
is in the 3 quadrant, only its Tangent is positive.
The Sine and Cosine of an angle in this quadrant are negative.
You can memorize this as All Students Take Calculus.
rd
π/2
π
S A
T
C
2π
3π/2
ALGEBRA: For 2 equations, use substitution (getting one unknown in terms of the other) or elimination (stacking equations
and combining them). Quadratic equations usually get factored. Word Problems: Create equations using letters to represent
unknown values and then solve. You may need to use a formula such as Average = Sum/ # of terms or Rate = Distance/Time.
NOTE: If the choices are known values, consider backsolving. If they’re unknown values, consider picking numbers.
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Exponents: 37 x 34 = 311 (37)4 = 328
31/2 = √3
Negative exponents invert: 3-1 = 1/3.
3
b
Logs: log2 8 = 3 is the same as 2 = 8. loga (7 )= b loga 7
loga (pq) = loga p + loga q
Imaginary numbers: i = the square roof of negative 1.
i2 = -1; i3 = -i; i4 = 1
Irrational numbers go on forever without repeating. They cannot be expressed as fractions.
The Probability of Event A and Event B both occurring is the product of their individual probabilities.
Permutations: There are 6! ways or arranging 6 things. There are 6 x 5 ways of arranging 6 things, two at a time.
Expected Value: Multiply rows; then add the products. Matrix Product: # of columns on left must equal # of rows on right.
Waves: Frequency (period) = Length of one cycle. Amplitude = height.
Domain refers to all possible x-value. Range refers to all possible y-values.
Component Form (vectors): i = horizontal distance; j = vertical distance.
Logic: If you know that “If A then B” is true, so is “If not B then not A.” (Reverse and negate.)