Daily Practice · Higher Plus
February 1953 5-a-day
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The batch download puts all 5 tiers' February 1953 sheets in a single PDF, each tier behind its own divider page - 140 sheets in one file.
Every sheet in February 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st February 1953x = 173 and y = 148, each correct to the nearest whole number. Work out the upper bound of x - y.
- 2nd February 1953Solve x^2 - 3x - 4 < 0.
- 3rd February 1953y is directly proportional to sqrt(x). When x = 36, y = 54. Work out y when x = 9.
- 4th February 1953A cuboid measures 12 cm by 14 cm by 5 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 5th February 1953A bag holds 4 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 6th February 1953On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th February 1953A car covers 600 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 8th February 1953Write x^2 + 14x - 3 in the form (x + a)^2 + b.
- 9th February 1953A train slows steadily from 25 m/s to rest in 4 seconds. Work out its deceleration.
- 10th February 1953A cuboid measures 8 cm by 12 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 11th February 1953A bag holds 4 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 12th February 1953A histogram has two bars: one 5 units wide with frequency density 1.5, one 10 units wide with density 3. How many values in total?
- 13th February 1953Rationalise the denominator of 9/sqrt(3), giving your answer in its simplest form.
- 14th February 1953Work out the coordinates of the turning point of y = x^2 + 16x - 5.
- 15th February 1953y is inversely proportional to x^2. When x = 4, y = 108. Work out y when x = 6.
- 16th February 1953The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 17th February 1953A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 1/12. Work out r.
- 18th February 1953On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 19th February 1953Simplify sqrt(12) + sqrt(108), giving your answer in the form a sqrt(b).
- 20th February 1953Simplify (x^2 - 11x + 30)/(x - 5).
- 21st February 1953y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 5.
- 22nd February 1953In a circle theorem proof, a step uses the fact that the alternate segment theorem is being proved. State the reason being quoted.
- 23rd February 1953The probability of winning a game is 1/10. A player expects 4 wins. How many games did they play?
- 24th February 1953A histogram has two bars: one 10 units wide with frequency density 1.5, one 25 units wide with density 3.5. How many values in total?
- 25th February 1953A rectangle is 10 cm by 15 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 26th February 1953In an algebraic proof, how would you write the square of an odd number in terms of an integer n?
- 27th February 1953y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 25.
- 28th February 1953In a vector proof you find that vector PQ = 6a + b and vector RS = 12a + 2b. What does this show about PQ and RS?