Daily Practice · Higher Plus
January 1969 5-a-day
Printing for a group?
The batch download puts all 5 tiers' January 1969 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in January 1969
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st January 1969On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 2nd January 1969Simplify sqrt(80) + sqrt(125), giving your answer in the form a sqrt(b).
- 3rd January 1969Solve x^2 - 16 < 0.
- 4th January 1969A train slows steadily from 17 m/s to rest in 4 seconds. Work out its deceleration.
- 5th January 1969In a vector proof you find that vector PQ = 2a - 3b and vector RS = 6a - 9b. What does this show about PQ and RS?
- 6th January 1969A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 7th January 1969A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 1.4. How many values in total?
- 8th January 1969A rectangle is 16 cm by 27 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th January 1969Write x^2 + 2x - 11 in the form (x + a)^2 + b.
- 10th January 1969y is inversely proportional to x^2. When x = 2, y = 18. Work out y when x = 3.
- 11th January 1969A cuboid measures 12 cm by 12 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 12th January 1969A bag holds 5 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 13th January 1969On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 14th January 1969Expand and simplify (3 + sqrt(7))(3 - sqrt(7)).
- 15th January 1969Work out the coordinates of the turning point of y = x^2 + 8x - 7.
- 16th January 1969y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 5.
- 17th January 1969A cuboid measures 11 cm by 7 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 18th January 1969A bag holds 3 red, 5 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 19th January 1969A histogram has two bars: one 5 units wide with frequency density 2.5, one 10 units wide with density 3.5. How many values in total?
- 20th January 1969A block has mass 470 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st January 1969Simplify (x^2 + 12x + 32)/(x + 4).
- 22nd January 1969y is directly proportional to sqrt(x). When x = 4, y = 10. Work out y when x = 81.
- 23rd January 1969The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 24th January 1969A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 25th January 1969On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 26th January 1969x = 199 and y = 177, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th January 1969In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 28th January 1969A train slows steadily from 22 m/s to rest in 8 seconds. Work out its deceleration.
- 29th January 1969In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 30th January 1969The probability of winning a game is 1/2. A player expects 12 wins. How many games did they play?
- 31st January 1969A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?