Daily Practice · Higher Plus
January 1954 5-a-day
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The batch download puts all 5 tiers' January 1954 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1954A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd January 1954A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 1.4. How many values in total?
- 3rd January 1954x = 107 and y = 13, each correct to the nearest whole number. Work out the upper bound of x - y.
- 4th January 1954Make x the subject of 3x + 6 = y(x + 6).
- 5th January 1954y is directly proportional to sqrt(x). When x = 4, y = 18. Work out y when x = 16.
- 6th January 1954A cuboid measures 4 cm by 10 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th January 1954A bag holds 4 red, 6 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th January 1954On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 9th January 1954A car covers 270 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 10th January 1954Write 3/(x + 3) + 7/(x - 4) as a single fraction.
- 11th January 1954A train slows steadily from 36 m/s to rest in 10 seconds. Work out its deceleration.
- 12th January 1954The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 13th January 1954A bag holds 9 counters, r of them red. Two are taken without replacement and P(both red) = 5/18. Work out r.
- 14th January 1954A histogram has two bars: one 20 units wide with frequency density 1.5, one 10 units wide with density 1.4. How many values in total?
- 15th January 1954Rationalise the denominator of 25/sqrt(5), giving your answer in its simplest form.
- 16th January 1954Solve 16x^2 + 16x - 5 = 0.
- 17th January 1954y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 18th January 1954In a circle theorem proof, a step uses the fact that the exterior angle of a cyclic quadrilateral is being found. State the reason being quoted.
- 19th January 1954The probability of winning a game is 4/5. A player expects 56 wins. How many games did they play?
- 20th January 1954On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 21st January 1954Simplify sqrt(80) + sqrt(180), giving your answer in the form a sqrt(b).
- 22nd January 1954f(x) = 8x - 8. Work out the inverse function f^-1(x).
- 23rd January 1954y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 3.
- 24th January 1954In a vector proof you find that vector PQ = 6a + 2b and vector RS = 24a + 8b. What does this show about PQ and RS?
- 25th January 1954A bag holds 6 red and n blue counters. The probability of taking a red is 6/11. Work out n.
- 26th January 1954A histogram has two bars: one 5 units wide with frequency density 1.2, one 20 units wide with density 0.6. How many values in total?
- 27th January 1954A rectangle is 27 cm by 6 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 28th January 1954Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 29th January 1954y is directly proportional to sqrt(x). When x = 25, y = 25. Work out y when x = 4.
- 30th January 1954A cuboid measures 3 cm by 15 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 31st January 1954A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?