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SIFT practice questions

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Question 1Simple Drawings

A simple line drawing is rotated 90° clockwise and then a further 180° clockwise. A single rotation that gives the same final image is

  1. 270° clockwise Correct answer.
  2. 180° counterclockwise
  3. 90° clockwise
  4. 360° clockwise

Explanation

Turns made in the same direction simply add together, so the total is 90° + 180° = 270° clockwise. A 270° clockwise turn lands on the same orientation as 90° counterclockwise, so the single equivalent turn is 270° clockwise.

Question 2Simple Drawings

A rotation of 270° clockwise is equivalent to a rotation of

  1. 45° counterclockwise
  2. 270° counterclockwise
  3. 180° counterclockwise
  4. 90° counterclockwise Correct answer.

Explanation

A clockwise turn and a counterclockwise turn of complementary size reach the same orientation, because 270° + 90° = 360°. So turning 270° clockwise looks exactly like turning 90° the other way.

Question 3Simple Drawings

A drawing of an arrow points straight up the page. After a 90° counterclockwise rotation, the arrow points

  1. right
  2. down
  3. up
  4. left Correct answer.

Explanation

A quarter turn counterclockwise carries 'up' into 'left', just as the hour hand moving backward from 12 reaches 9. The arrow therefore points left after the turn.

Question 4Simple Drawings

Which feature of a simple drawing stays the same no matter how the drawing is rotated?

  1. The edge of the page nearest to it
  2. The direction each line points
  3. Its position on the page
  4. Its size and proportions Correct answer.

Explanation

Rotation is a rigid motion: it changes orientation and location but preserves all lengths, angles, and proportions. Only the orientation and placement of the drawing change.

Question 5Simple Drawings

When a simple drawing is flipped over a mirror line, the result is

  1. its mirror image Correct answer.
  2. a smaller copy
  3. a rotated copy
  4. an enlarged copy

Explanation

Flipping a drawing over a line reverses its handedness, producing a mirror image. No rotation in the plane can reverse handedness, so the flipped result cannot be matched by turning the original.

Question 6Simple Drawings

On a clock face, how many hours of hand movement correspond to a 90° rotation?

  1. Nine hours
  2. Six hours
  3. Three hours Correct answer.
  4. One hour

Explanation

The dial divides 360° into twelve equal hours, so each hour covers 30°. A quarter turn of 90° therefore equals three hours of hand movement.

Question 7Simple Drawings

A dot is drawn at the top-left corner of a square drawing. The drawing is rotated 180°. The dot is now at

  1. the top-left corner
  2. the bottom-right corner Correct answer.
  3. the top-right corner
  4. the bottom-left corner

Explanation

A half turn sends every point straight through the center to the diagonally opposite position. A top-left corner therefore moves to the bottom-right corner.

Question 8Simple Drawings

A simple drawing of a plus sign made of two equal lines crossing at their midpoints looks exactly the same after which rotation?

  1. 180°
  2. 90° Correct answer.
  3. 60°
  4. 45°

Explanation

The two equal arms of a plus sign swap places under a quarter turn, so the figure maps onto itself at 90°. Other multiples of 90° also work, but 90° is the smallest such turn.

Question 9Simple Drawings

A point of a drawing lies at coordinates (3, −2) measured from the center of rotation. After a 180° rotation about that center, the point lies at

  1. (3, 2)
  2. (−3, −2)
  3. (−3, 2) Correct answer.
  4. (2, −3)

Explanation

A half turn about the center negates both coordinates, sending (x, y) to (−x, −y). Applying that rule to (3, −2) gives (−3, 2).

Question 10Simple Drawings

A drawing shows an L-shaped bar with a long arm pointing straight up from a corner and a short foot pointing right from the same corner. After a 90° clockwise rotation, the long arm points

  1. up
  2. down
  3. right Correct answer.
  4. left

Explanation

A quarter turn clockwise carries 'up' into 'right' and 'right' into 'down'. The long arm therefore ends up pointing right while the short foot points down.

Question 11Simple Drawings

Three marked points on a drawing run in clockwise order around the figure. After any rotation of the drawing, those points run

  1. in an order that cannot be predicted
  2. in clockwise order only if the rotation is less than 180°
  3. in clockwise order Correct answer.
  4. in counterclockwise order

Explanation

Rotation preserves the cyclic order of points around a figure, so clockwise stays clockwise for every angle of turn. Only a reflection reverses the order into counterclockwise.

Question 12Simple Drawings

A drawing is rotated a total of 450° clockwise. The result looks the same as a rotation of

  1. 45° clockwise
  2. 270° clockwise
  3. 90° clockwise Correct answer.
  4. 180° clockwise

Explanation

Orientations repeat every full turn, so subtract whole 360° turns from the total: 450° − 360° = 90°. The extra 90° beyond one full turn is all that shows.

Question 13Simple Drawings

The capital letter M is rotated 180° in the plane. The result most closely resembles the capital letter

  1. E
  2. Z
  3. N
  4. W Correct answer.

Explanation

A half turn turns the letter upside down, so the M's two peaks now point downward and its outer strokes open upward. That upside-down outline matches a W.

Question 14Simple Drawings

A drawing is reflected across a vertical line through its center and then across a horizontal line through the same center. The combined effect is the same as

  1. a 180° rotation Correct answer.
  2. a reflection across a diagonal line
  3. a 90° rotation
  4. no change at all

Explanation

Reflecting across one line and then across a perpendicular line is equivalent to a half turn about their intersection. Two reflections also restore handedness, which is why the result is a rotation rather than a reflection.

Question 15Simple Drawings

In these items a drawing is rotated about its own center. Which point of the drawing stays where it is during the turn?

  1. The center point Correct answer.
  2. The topmost point
  3. The point farthest from the center
  4. The leftmost point

Explanation

Under a rotation about a point, that point is the only fixed point; every other point sweeps along an arc. So the center of rotation is the one point that does not move.

Question 16Simple Drawings

A parallelogram with no right angles is turned about its center. It will look exactly the same as the original after a rotation of

  1. 180° Correct answer.
  2. 90°
  3. 270°
  4. 45°

Explanation

A slanted parallelogram has half-turn symmetry: a 180° turn maps it onto itself, while no quarter turn can. This is the same two-fold symmetry an S shape has.

Question 17Simple Drawings

A small notch sits at the middle of the top edge of a square drawing. In a second copy the notch sits at the middle of the right edge. The change between the copies could be a rotation of

  1. 90° counterclockwise
  2. 180°
  3. 45° clockwise
  4. 90° clockwise Correct answer.

Explanation

Moving a feature from the top edge to the right edge is one quarter turn clockwise, the same motion as the hour hand from 12 to 3. The notch stays centred on an edge, which confirms a quarter turn.

Question 18Simple Drawings

A drawing is rotated 120° clockwise, then another 120° clockwise, then another 120° clockwise. The final image

  1. is turned 90° from the original
  2. matches the original exactly Correct answer.
  3. is turned 180° from the original
  4. is a mirror image of the original

Explanation

Three turns of 120° add to 360°, which is one full revolution. A full turn returns every point to its starting place, so the final image coincides with the original.

Question 19Simple Drawings

A drawing is rotated 90° clockwise and then 270° counterclockwise. The net effect is a rotation of

  1. 180° Correct answer.
  2. 90° clockwise
  3. 270° clockwise
  4. 360°

Explanation

Opposite-direction turns partly cancel, so subtract the smaller from the larger: 270° − 90° = 180°. The leftover 180° acts in the counterclockwise direction, which is the same as a plain half turn.

Question 20Simple Drawings

One copy of a drawing is turned 90° clockwise from the original, and a second copy is turned 270° clockwise from the original. The angle between the two copies is

  1. 180° Correct answer.
  2. 0°
  3. 90°
  4. 270°

Explanation

Both copies are measured from the same starting drawing, so the gap between them is found by subtracting: 270° − 90° = 180°. They therefore appear upside down relative to each other.

Question 21Simple Drawings

A drawing is reflected across the vertical line through its center and then rotated 180° about that center. The result is the same as reflecting the original across

  1. the horizontal line through its center Correct answer.
  2. a line at 45° to the horizontal
  3. no line at all, since the result is a pure rotation
  4. the same vertical line

Explanation

The vertical reflection sends (x, y) to (−x, y), and the half turn then sends that to (x, −y). The map (x, y) → (x, −y) is exactly a reflection across the horizontal line through the center.

Question 22Simple Drawings

A drawing is rotated 90° clockwise about its center, and the result is then reflected across the vertical line through that center. The final image is the original reflected across

  1. the horizontal line
  2. the line y = −x Correct answer.
  3. the line y = x
  4. the vertical line

Explanation

The clockwise quarter turn sends (x, y) to (y, −x); the vertical reflection then sends that to (−y, −x). The map (x, y) → (−y, −x) is precisely a reflection across the line y = −x.

Question 23Simple Drawings

A drawing is reflected across one line and then across a second line that meets the first at an angle of 45°. The combined effect is a rotation of

  1. 45°
  2. 90° Correct answer.
  3. 22.5°
  4. 180°

Explanation

Two reflections in lines meeting at angle θ compose to a rotation of 2θ about the point where the lines cross. With θ = 45°, the rotation is 90°.

Question 24Simple Drawings

A drawing of an upward-pointing arrow has a small notch on its left side. The arrow is rotated 90° clockwise, so that it now points right. The notch is on the

  1. right side
  2. bottom side
  3. left side
  4. top side Correct answer.

Explanation

A clockwise quarter turn carries 'up' to 'right' and 'left' to 'up'. Since the notch began on the left, it finishes on the top side of the arrow that now points right.

Question 25Simple Drawings

Two drawings look alike except that in one the three marked features run clockwise around the figure, while in the other the same three features run counterclockwise. The two drawings

  1. differ by a 90° rotation
  2. cannot be rotations of one another Correct answer.
  3. differ by a 180° rotation
  4. are identical after any rotation

Explanation

Every rotation preserves the cyclic order of features around a figure, so clockwise stays clockwise. A reversal to counterclockwise can only come from a reflection, meaning the two drawings are mirror images rather than rotated copies.

Question 26Simple Drawings

A simple drawing is reflected across a horizontal line. In the original, a small mark sits 3 cm above that line. In the reflected copy, the mark sits

  1. 3 cm below the line Correct answer.
  2. 6 cm below the line
  3. 3 cm above the line
  4. 6 cm above the original mark

Explanation

A reflection flips a figure to the opposite side of the mirror line while keeping each point the same distance from that line. The mark therefore stays 3 cm from the line but now lies below it.

Question 27Simple Drawings

A drawing lies on a square grid. A mirror line runs diagonally through the grid points (0, 0), (1, 1), (2, 2) and so on. A dot of the drawing sits at (5, 2). After the drawing is reflected in this line, the dot sits at

  1. (2, 5) Correct answer.
  2. (-5, 2)
  3. (5, -2)
  4. (-2, -5)

Explanation

A mirror line through (0, 0), (1, 1), (2, 2) is the line y = x, and reflecting in it exchanges the two coordinates of every point. So (5, 2) becomes (2, 5).

Question 28Simple Drawings

A drawing is reflected across a vertical line, and the image is then reflected across a second vertical line that lies 4 cm to the right of the first. The final image is

  1. identical to the original drawing
  2. the original shifted 8 cm to the right Correct answer.
  3. the original turned 180° about the midpoint between the two lines
  4. the original shifted 4 cm to the right

Explanation

Two reflections in parallel mirror lines combine to give a translation perpendicular to those lines. The shift equals twice the gap between the lines, so it is 2 × 4 cm = 8 cm, in the direction from the first line to the second.

Question 29Hidden Figures

Who is the author of the book Hidden Figures?

  1. Mary Jackson
  2. Dorothy Vaughan
  3. Katherine Johnson
  4. Margot Lee Shetterly Correct answer.

Explanation

Margot Lee Shetterly wrote the 2016 nonfiction book Hidden Figures, which chronicles the contributions of Black women mathematicians at Langley. The other names belong to women featured in the book, not to its author.

Question 30Hidden Figures

Which federal agency employed the women featured in Hidden Figures?

  1. NSA
  2. NASA Correct answer.
  3. CIA
  4. FBI

Explanation

The women worked at Langley Memorial Aeronautical Laboratory for NACA, which became NASA in 1958. Their calculations supported aeronautics and spaceflight programs.

Question 31Hidden Figures

Which mathematician verified the calculations for John Glenn's Friendship 7 orbital mission?

  1. Mary Jackson
  2. Dorothy Vaughan
  3. Christine Darden
  4. Katherine Johnson Correct answer.

Explanation

John Glenn specifically asked that Katherine Johnson check the electronic computer's results before his flight. Her reputation for accuracy made her the person he trusted.

Question 32Hidden Figures

Who became NASA's first Black female engineer?

  1. Mary Jackson Correct answer.
  2. Katherine Johnson
  3. Dorothy Vaughan
  4. Christine Darden

Explanation

Mary Jackson completed additional engineering coursework and was promoted to engineer in 1958. This made her NASA's first Black female engineer.

Question 33Hidden Figures

What name was given to the group of African-American female mathematicians at Langley?

  1. West Area Computers Correct answer.
  2. Langley Aeronautics Team
  3. Human Calculators Union
  4. Mercury Seven

Explanation

The segregated group of Black women who performed mathematical work at Langley was known as the West Area Computers. They handled calculations for engineers and researchers.

Question 34Hidden Figures

Which woman taught herself the FORTRAN programming language and trained her staff in it?

  1. Dorothy Vaughan Correct answer.
  2. Katherine Johnson
  3. Mary Jackson
  4. Christine Darden

Explanation

Dorothy Vaughan recognized that electronic computers would replace manual calculation and learned FORTRAN on her own. She then taught programming skills to the women she supervised.

Question 35Hidden Figures

What was the name of John Glenn's 1962 spacecraft?

  1. Friendship 7 Correct answer.
  2. Apollo 11
  3. Freedom 7
  4. Mercury Atlas

Explanation

John Glenn orbited Earth aboard Friendship 7 in 1962. Katherine Johnson verified the trajectory calculations for that mission.

Question 36Hidden Figures

What did Miriam Mann repeatedly remove from the Langley cafeteria?

  1. A time clock
  2. A menu board
  3. A fire alarm
  4. A 'colored' sign Correct answer.

Explanation

Miriam Mann removed the sign that marked the segregated table in the cafeteria. She kept taking it down even when it was replaced.

Question 37Hidden Figures

In 1949, Dorothy Vaughan became acting supervisor of which group?

  1. Flight Research Division
  2. Apollo Program
  3. Mercury Seven
  4. West Area Computers Correct answer.

Explanation

Dorothy Vaughan became acting supervisor of the West Area Computers in 1949, making her the first Black supervisor at NACA. She led the group through the transition to electronic computing.

Question 38Hidden Figures

Mary Jackson had to petition a court for permission to do what?

  1. Travel to space
  2. Enroll at NASA
  3. Attend Hampton High School night classes Correct answer.
  4. Join the military

Explanation

Mary Jackson needed court approval to attend night classes at Hampton High School, which was then whites-only. Completing those courses was necessary for her engineering promotion.

Question 39Hidden Figures

Which award did Katherine Johnson receive in 2015?

  1. Nobel Prize in Physics
  2. Congressional Space Medal of Honor
  3. Presidential Medal of Freedom Correct answer.
  4. Turing Award

Explanation

President Barack Obama awarded Katherine Johnson the Presidential Medal of Freedom in 2015. It recognized her contributions to spaceflight calculations.

Question 40Hidden Figures

Christine Darden is known for research on what phenomenon?

  1. Sonic boom Correct answer.
  2. Satellite orbits
  3. Rocket propulsion
  4. Lunar landing

Explanation

Christine Darden conducted research on supersonic aircraft and sonic booms at Langley. Her work helped engineers understand and reduce the effects of sonic booms.

Question 41Hidden Figures

NACA was renamed NASA in which year?

  1. 1945
  2. 1972
  3. 1969
  4. 1958 Correct answer.

Explanation

The National Advisory Committee for Aeronautics became the National Aeronautics and Space Administration in 1958. This transition expanded the agency's role in space exploration.

Question 42Hidden Figures

Katherine Johnson graduated from West Virginia State College at what age?

  1. 24
  2. 21
  3. 18 Correct answer.
  4. 15

Explanation

Katherine Johnson enrolled in college at 15 and graduated at 18. Her early academic success was notable in a time of limited opportunities for Black students.

Question 43Hidden Figures

What did John Glenn say when told to trust the electronic computer's calculations?

  1. Get the girl to check the numbers. Correct answer.
  2. I trust the machine.
  3. Ask the President.
  4. Launch without me.

Explanation

Glenn insisted that Katherine Johnson verify the computer's output before he flew. His statement reflected the confidence engineers had in her manual calculations.

Question 44Hidden Figures

After leaving engineering, Mary Jackson worked in what role at NASA?

  1. Equal opportunity specialist Correct answer.
  2. Flight director
  3. Astronaut trainer
  4. Public affairs officer

Explanation

Mary Jackson later became an equal opportunity specialist at NASA. In that role she worked on hiring and promotion issues affecting women and minorities.

Question 45Hidden Figures

Dorothy Vaughan retired from NASA in which year?

  1. 1980
  2. 1971 Correct answer.
  3. 1969
  4. 1958

Explanation

Dorothy Vaughan retired from NASA in 1971 after a long career at Langley. She had moved from manual computing into programming and supervision.

Question 46Hidden Figures

The West Area Computers primarily performed which task?

  1. Mathematical calculations Correct answer.
  2. Designing rockets
  3. Managing budgets
  4. Piloting aircraft

Explanation

The West Area Computers were human computers who performed mathematical calculations for engineers and researchers. Their work supported aeronautics and spaceflight projects.

Question 47Hidden Figures

Apollo 11 landed on the Moon in which year?

  1. 1965
  2. 1962
  3. 1972
  4. 1969 Correct answer.

Explanation

Apollo 11 landed on the Moon in 1969. Katherine Johnson's trajectory work contributed to the mission's success.

Question 48Hidden Figures

What did the book's subtitle say the women helped win?

  1. The Space Race Correct answer.
  2. The Cold War
  3. The Civil War
  4. World War II

Explanation

The subtitle identifies the women as Black mathematicians who helped win the Space Race. Their calculations supported American spaceflight during the Cold War competition.

Question 49Hidden Figures

Katherine Johnson contributed to Apollo 13 by doing what?

  1. Designing the lunar module
  2. Selecting the landing site
  3. Piloting the command module
  4. Providing backup navigation procedures Correct answer.

Explanation

After the Apollo 13 explosion, Katherine Johnson provided backup navigation procedures that helped the crew return safely. Her work supported the mission's emergency recovery.

Question 50Hidden Figures

Christine Darden was the first Black woman at Langley to be promoted into what?

  1. Astronaut Corps
  2. Mercury Seven
  3. Senior Executive Service Correct answer.
  4. National Academy of Engineering

Explanation

Christine Darden became the first Black woman at Langley promoted into the Senior Executive Service. This recognized her leadership in aeronautics research.