Daily Practice · Higher Plus
January 1965 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1965 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1965
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1965A train slows steadily from 37 m/s to rest in 10 seconds. Work out its deceleration.
- 2nd January 1965A cuboid measures 10 cm by 8 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 3rd January 1965A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 4th January 1965A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 0.8. How many values in total?
- 5th January 1965Expand and simplify (9 + sqrt(3))(9 - sqrt(3)).
- 6th January 1965The point (2, -2) lies on y = f(x). Write down its image on y = f(x) - 5.
- 7th January 1965y is inversely proportional to x^2. When x = 2, y = 108. Work out y when x = 6.
- 8th January 1965A cuboid measures 6 cm by 10 cm by 7 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 9th January 1965A bag holds 5 red, 5 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 10th January 1965On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 11th January 1965A block has mass 450 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 12th January 1965Prove that the sum of 4 consecutive integers is always a multiple of 2. State the simplified sum you would use.
- 13th January 1965y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 2.
- 14th January 1965The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 15th January 1965A bag holds 10 counters, r of them red. Two are taken without replacement and P(both red) = 28/45. Work out r.
- 16th January 1965A histogram has two bars: one 5 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 17th January 1965x = 140 and y = 78, each correct to the nearest whole number. Work out the upper bound of x - y.
- 18th January 1965f(x) = 4x - 2 and g(x) = 5x - 8. Work out fg(-3).
- 19th January 1965y is directly proportional to sqrt(x). When x = 25, y = 35. Work out y when x = 16.
- 20th January 1965In 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.
- 21st January 1965The probability of winning a game is 1/5. A player expects 8 wins. How many games did they play?
- 22nd January 1965On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 23rd January 1965A car covers 890 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 January 1965The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 25th January 1965A train slows steadily from 25 m/s to rest in 10 seconds. Work out its deceleration.
- 26th January 1965In a vector proof you find that vector PQ = 6a - 2b and vector RS = 24a - 8b. What does this show about PQ and RS?
- 27th January 1965A bag holds 7 red and n blue counters. The probability of taking a red is 7/12. Work out n.
- 28th January 1965A histogram has two bars: one 5 units wide with frequency density 0.4, one 5 units wide with density 0.8. How many values in total?
- 29th January 1965Rationalise the denominator of 55/sqrt(11), giving your answer in its simplest form.
- 30th January 1965A quadratic sequence starts 15, 33, 59, 93. Work out the second difference, and the coefficient of n^2.
- 31st January 1965y is inversely proportional to x^2. When x = 2, y = 144. Work out y when x = 6.