Daily Practice · Higher Plus
March 1974 5-a-day
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The batch download puts all 5 tiers' March 1974 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1974
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1974Rationalise the denominator of 84/sqrt(7), giving your answer in its simplest form.
- 2nd March 1974f(x) = 6x + 9. Work out the inverse function f^-1(x).
- 3rd March 1974y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 4th March 1974In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 5th March 1974The probability of winning a game is 3/5. A player expects 33 wins. How many games did they play?
- 6th March 1974A histogram has two bars: one 20 units wide with frequency density 2, one 20 units wide with density 0.6. How many values in total?
- 7th March 1974Simplify sqrt(50) + sqrt(18), giving your answer in the form a sqrt(b).
- 8th March 1974Solve x^2 + y^2 = 25 and y = x - 1 simultaneously.
- 9th March 1974y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 9.
- 10th March 1974In a vector proof you find that vector PQ = 3a - 3b and vector RS = 12a - 12b. What does this show about PQ and RS?
- 11th March 1974A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 12th March 1974On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 13th March 1974A rectangle is 13 cm by 12 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th March 1974Use the iteration x(n+1) = cube root of (4x(n) + 3) with x(0) = 1. Work out x(1) to 3 decimal places.
- 15th March 1974A train slows steadily from 22 m/s to rest in 10 seconds. Work out its deceleration.
- 16th March 1974A cuboid measures 4 cm by 7 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 17th March 1974A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 18th March 1974A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 0.8. How many values in total?
- 19th March 1974Expand and simplify (5 + sqrt(11))(5 - sqrt(11)).
- 20th March 1974Work out the nth term of the quadratic sequence 3, 12, 29, 54, ...
- 21st March 1974y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 22nd March 1974A cuboid measures 8 cm by 14 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 23rd March 1974A bag holds 6 red, 6 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 24th March 1974On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 25th March 1974A block has mass 810 g (to the nearest 10 g) and volume 23 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th March 1974The point (-6, -4) lies on y = f(x). Write down its image on y = f(-x).
- 27th March 1974y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 28th March 1974The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 29th March 1974A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 36/55. Work out r.
- 30th March 1974A histogram has two bars: one 5 units wide with frequency density 2.5, one 25 units wide with density 3. How many values in total?
- 31st March 1974x = 140 and y = 94, each correct to the nearest whole number. Work out the upper bound of x - y.