Daily Practice · Higher Plus
February 1972 5-a-day
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The batch download puts all 5 tiers' February 1972 sheets in a single PDF, each tier behind its own divider page - 145 sheets in one file.
Every sheet in February 1972
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1972A cuboid measures 7 cm by 13 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd February 1972A bag holds 6 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd February 1972On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 4th February 1972Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
- 5th February 1972Write x^2 + 8x + 13 in the form (x + a)^2 + b.
- 6th February 1972A train slows steadily from 24 m/s to rest in 4 seconds. Work out its deceleration.
- 7th February 1972The point (6, 8) lies on the circle x^2 + y^2 = 100. Work out the gradient of the tangent to the circle at that point.
- 8th February 1972A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 9th February 1972A histogram has two bars: one 20 units wide with frequency density 1.2, one 10 units wide with density 1.4. How many values in total?
- 10th February 1972Simplify sqrt(80) + sqrt(20), giving your answer in the form a sqrt(b).
- 11th February 1972Work out the coordinates of the turning point of y = x^2 + 8x - 4.
- 12th February 1972y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 13th February 1972In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 14th February 1972The probability of winning a game is 1/8. A player expects 7 wins. How many games did they play?
- 15th February 1972On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th February 1972A rectangle is 17 cm by 9 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 17th February 1972Simplify (x^2 - 2x - 24)/(x + 4).
- 18th February 1972y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 19th February 1972In a vector proof you find that vector PQ = 5a - 5b and vector RS = 15a - 15b. What does this show about PQ and RS?
- 20th February 1972A bag holds 6 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 21st February 1972A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 22nd February 1972Expand and simplify (5 + sqrt(5))(5 - sqrt(5)).
- 23rd February 1972In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 24th February 1972y is directly proportional to sqrt(x). When x = 49, y = 28. Work out y when x = 81.
- 25th February 1972A cuboid measures 8 cm by 13 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th February 1972A bag holds 3 red and 10 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th February 1972On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 28th February 1972A block has mass 520 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 29th February 1972Make x the subject of 2x + 5 = y(x + 5).