Daily Practice · Higher Plus
March 1963 5-a-day
Printing for a group?
The batch download puts all 5 tiers' March 1963 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in March 1963
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st March 1963A train slows steadily from 38 m/s to rest in 5 seconds. Work out its deceleration.
- 2nd March 1963In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 3rd March 1963The probability of winning a game is 1/10. A player expects 15 wins. How many games did they play?
- 4th March 1963A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 1.4. How many values in total?
- 5th March 1963Expand and simplify (3 + sqrt(7))(3 - sqrt(7)).
- 6th March 1963Work out the coordinates of the turning point of y = x^2 - 2x - 8.
- 7th March 1963y is inversely proportional to x^2. When x = 4, y = 100. Work out y when x = 5.
- 8th March 1963In a vector proof you find that vector PQ = 6a + 3b and vector RS = 12a + 6b. What does this show about PQ and RS?
- 9th March 1963A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 10th March 1963On 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?
- 11th March 1963A block has mass 220 g (to the nearest 10 g) and volume 18 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th March 1963Simplify (x^2 - 5x - 14)/(x + 2).
- 13th March 1963y is directly proportional to x^3. When x = 4, y = 128. Work out y when x = 2.
- 14th March 1963A cuboid measures 8 cm by 7 cm by 7 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th March 1963A bag holds 4 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th March 1963A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.6. How many values in total?
- 17th March 1963x = 75 and y = 24, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th March 1963In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 19th March 1963y is directly proportional to sqrt(x). When x = 25, y = 45. Work out y when x = 16.
- 20th March 1963A cuboid measures 14 cm by 11 cm by 8 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st March 1963A bag holds 7 red, 4 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd March 1963On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 23rd March 1963A car covers 430 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 24th March 1963Make x the subject of 6x + 2 = y(x + 2).
- 25th March 1963A train slows steadily from 39 m/s to rest in 10 seconds. Work out its deceleration.
- 26th March 1963The point (8, 15) lies on the circle x^2 + y^2 = 289. Work out the gradient of the tangent to the circle at that point.
- 27th March 1963A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/28. Work out r.
- 28th March 1963A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 29th March 1963Rationalise the denominator of 40/sqrt(5), giving your answer in its simplest form.
- 30th March 1963Write 5/(x - 5) + 3/(x + 3) as a single fraction.
- 31st March 1963y is inversely proportional to x^2. When x = 5, y = 36. Work out y when x = 6.